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Similar Question 1
<p>The revenue function for a production by a theatre group is <code class='latex inline'>R(t) = -50t^2 + 300t</code>, where t is the ticket price in dollars. The cost function for the production is <code class='latex inline'>C(t) = 600 - 50t</code>. Determine the ticket price that will allow the production to break even.</p>
Similar Question 2
<p>Determine the coordinates of the point(s) of intersection of each linear-quadratic system algebraically.</p><p><code class='latex inline'>y = \frac{1}{2}x^2 - 2x - 3</code> and <code class='latex inline'>y = -3x + 1</code></p>
Similar Question 3
<p>In the diagram, the line <code class='latex inline'>y = x + 1</code> intersects the parabola <code class='latex inline'>y = x^2 - 3x - 4</code> at the points P and Q. Determine the coordinates of P and Q.</p><img src="/qimages/236" />
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>The line x = 2 intersects the quadratic function <code class='latex inline'>y = x^2- 9</code> at one point, (2, -5). Explain why the line x = 2 is not considered a tangent line to the quadratic</p>
<p>Calculate the point(s) of intersection of </p><p><code class='latex inline'>f(x) = 2x^2 + 4x - 11</code> and <code class='latex inline'>g(x) = -3x + 4</code>.</p>
<p>In the diagram, the line <code class='latex inline'>y = x + 1</code> intersects the parabola <code class='latex inline'>y = x^2 - 3x - 4</code> at the points P and Q. Determine the coordinates of P and Q.</p><img src="/qimages/236" />
<p>Determine the coordinates of the point(s) of intersection of each linear-quadratic system algebraically.</p><p><code class='latex inline'>y = \frac{1}{2}x^2 - 2x - 3</code> and <code class='latex inline'>y = -3x + 1</code></p>
<p>Determine if each quadratic function will intersect once, twice, or not at all with the given linear function.</p><p><code class='latex inline'>y = -\frac{2}{3}x^2 + x + 3</code> and <code class='latex inline'>y = x </code></p>
<p>Verify the solutions to below using a graphing device or by substituting into the original equations.</p><p><code class='latex inline'>y=-\dfrac{2}{3}x^2+x+3</code> and <code class='latex inline'>y=x</code></p>
<p>Find the point(s) of intersection of the line <code class='latex inline'>y = 7x - 42</code> and the circle <code class='latex inline'>x^2 + y^2 -4x + 6y =12</code>.</p>
<p>Determine if each quadratic function will intersect once, twice, or not at all with the given linear function.</p><p><code class='latex inline'>y = \frac{1}{2}x^2 + 4x - 2</code> and <code class='latex inline'>y = x + 3</code></p>
<p>Determine the point(s) of intersection of each pair of functions.</p><p><code class='latex inline'>f(x) = -2x^2 - 5x + 20, g(x) = 6x - 1</code></p>
<p>Verify the solutions to below using a graphing device or by substituting into the original equations.</p><p><code class='latex inline'>y = x^2 - 7x + 15</code> and <code class='latex inline'>y = 2x -5</code></p>
<p>Find the point(s) of intersection by graphing.</p><p><code class='latex inline'>f(x) = 3x^2 - 2x - 1, g(x) = - x - 6</code></p>
<p>Find the point(s) of intersection by graphing.</p><p><code class='latex inline'>f(x) = -x^2 + 6x - 5, g(x) = -4x + 19</code></p>
<p>Determine the points of intersection of each pair of functions.</p><p><code class='latex inline'>y = 4x^2 - 15x + 20</code> and <code class='latex inline'>y = 5x - 4</code></p>
<p>Solve the system by substitution method.</p><p><code class='latex inline'>y = x^2</code></p><p><code class='latex inline'>y = x + 12</code></p>
<p>Determine the point(s) of intersection of each pair of functions.</p><p><code class='latex inline'>f(x) = -4x^2 - 2x + 3, g(x) = 5x + 4</code></p>
<p>Find the point(s) of intersection by graphing.</p><p><code class='latex inline'>f(x) = 2x^2 -1, g(x) =3x + 1</code></p>
<p>Determine the coordinates of the point(s) of intersection of each linear-quadratic system algebraically.</p><p><code class='latex inline'>y = -2x^2 - 7x + 10</code> and <code class='latex inline'>y = -x + 2</code></p>
<p>Determine the break-even points of the profit function <code class='latex inline'>P(x) = -2x^2 + 7x + 8</code>, where <code class='latex inline'>x</code> is the number of dirt bikes reduced, in thousands.</p>
<p>Find the point(s) of intersection by graphing.</p><p><code class='latex inline'>f(x) = x^2, g(x) = x + 6</code></p>
<p>The revenue function for a production by a theatre group is <code class='latex inline'>R(t) = -50t^2 + 300t</code>, where t is the ticket price in dollars. The cost function for the production is <code class='latex inline'>C(t) = 600 - 50t</code>. Determine the ticket price that will allow the production to break even.</p>
<p>Find the equation of the line which is tangent to the given parabola and has the given slope.</p><p><code class='latex inline'>y=-2x^2+5x + 4</code> and a line with a slope of <code class='latex inline'>1</code>.</p>
<p>The UV index on a sunny day can be modelled by the function <code class='latex inline'>f(x) =-0.15(x - 13)^2+ 7.6</code>, where <code class='latex inline'>x</code> represents the time of day on a 24-h clock and <code class='latex inline'>f(x)</code> represents the UV index. Between what hours was the UV index greater than <code class='latex inline'>7</code>?</p>
<p>A engineer is designing a parabolic arch. The arch must be 15 m high, and 6 m wide at a height of 8 m. </p><p>Determine a quadratic function that satisfies these conditions.</p>
<p>Determine the value of k in <code class='latex inline'>y = -x^2 + 4x + k</code> that will result in the intersection of the line <code class='latex inline'>y = 8x - 2</code> with the quadratic at</p><p> one point </p>
<p>Determine the value of k in <code class='latex inline'>y = -x^2 + 4x + k</code> that will result in the intersection of the line <code class='latex inline'>y = 8x - 2</code> with the quadratic at</p><p>two points </p>
<p>Determine the coordinates of all points of intersection of the functions <code class='latex inline'>x^2- 2x + 3y + 6 = 0</code> and <code class='latex inline'>4x + 6y + 12 = 0</code>.</p>
<p>Determine the coordinates of the point(s) of intersection of each linear-quadratic system algebraically.</p><p><code class='latex inline'>y = 3x^2 - 16x + 37</code> and <code class='latex inline'>y = 8x + 1</code></p>
<p>Determine the number of points of intersection <code class='latex inline'>f(x) = 4x^2 + x -3</code> and <code class='latex inline'>g(x) = 5x - 4</code> without solving.</p>
<p>An integer is two more than another integer. Twice the larger integer is one more than the square of the smaller integer. Find the two integers.</p>
<p>Determine the coordinates of the point(s) of intersection of each linear-quadratic system algebraically.</p><p><code class='latex inline'>y = x^2 - 7x + 15</code> and <code class='latex inline'>y = 2x -5</code></p>
<p>A daredevil jumps off the CN Tower and falls freely for a several seconds before releasing his parachute. His height, <code class='latex inline'>h(t)</code>, in metres, <code class='latex inline'>t</code> seconds after jumping can be modelled by </p> <ul> <li><p><code class='latex inline'>h_1(t) = -4.9t^2 + t + 360</code> before he released his parachute; and </p></li> <li><p><code class='latex inline'>h_2(t) = -4t + 142</code> after he released his parachute.</p></li> </ul> <p>How long after jumping did the daredevil release his parachute?</p>
<p>Determine if each quadratic function will intersect once, twice, or not at all with the given linear function.</p><p><code class='latex inline'>y = -x^2 + 3x - 5</code> and <code class='latex inline'>y = -x - 1</code></p>
<p>Determine the points of intersection of each pair of functions.</p><p><code class='latex inline'>y = -2x^2 + 9x + 9</code> and <code class='latex inline'>y = -3x - 5</code></p>
<p>Determine if each quadratic function will intersect once, twice, or not at all with the given linear function.</p><p><code class='latex inline'>y = 2x^2 - 2x + 1</code> and <code class='latex inline'>y = 3x - 5</code></p>
<p>Determine the point(s) of intersection of each pair of functions.</p><p><code class='latex inline'>f(x) = 5x^2 + x -2, g(x) = -3x - 6</code></p>
<p>Find the equation of the line which is tangent to the given parabola and has the given slope.</p><p><code class='latex inline'>y=-x^2-5x - 5</code> and a line with a slope of <code class='latex inline'>-3</code></p>
<p>A engineer is designing a parabolic arch. The arch must be 15 m high, and 6 m wide at a height of 8 m. </p><p>What its the width of the arch at its base?</p>
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