3. Q3d
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Similar Question 1
<p><code class='latex inline'>x^2-6x+5=0</code> has two roots <code class='latex inline'>x = 1, 5</code>.</p><p><em>i)</em> What does above tell you about the graph of <code class='latex inline'>y=x^2-6x+5</code>?</p><p><em>ii)</em> Verify your answer for part ii) using the discriminant.</p>
Similar Question 2
<p>Use the discriminant to determine the number of roots for each equation.</p><p><code class='latex inline'>-2x^2+ 5x - 1= 0</code></p>
Similar Question 3
<p>Use the discriminant to determine the number of roots for each equation.</p><p><code class='latex inline'>9x^2 -12x + 4 = 0 </code></p>
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>Use the discriminant to determine the number of roots for each equation.</p><p><code class='latex inline'>-2x^2+ 5x - 1= 0</code></p>
<p>Determine whether the vertex of each parabola lies above, below, or on the x-axis. Explain how you know,</p><p> <code class='latex inline'>h=5t^2-30t+45</code></p>
<p>For what value(s) of <code class='latex inline'>k</code> does the equation <code class='latex inline'>y=5x^2+6x+k</code> have each number of roots?</p><p><em>a)</em> two real roots</p><p><em>b)</em> one real root</p><p><em>c)</em> no real roots</p>
<p>A parabola has equation <code class='latex inline'>y=4x^2+x+c</code>. One <code class='latex inline'>x</code>-intercept is —3. What is the value of <code class='latex inline'>c</code>?</p>
<p>Determine the values of <code class='latex inline'>k</code> for which the function <code class='latex inline'>f(x) = 4x^2 - 3x + 2kx + 1</code> has two zeros. Check these value in the original equation.</p>
<p><code class='latex inline'>x^2-6x+5=0</code> has two roots <code class='latex inline'>x = 1, 5</code>.</p><p><em>i)</em> What does above tell you about the graph of <code class='latex inline'>y=x^2-6x+5</code>?</p><p><em>ii)</em> Verify your answer for part ii) using the discriminant.</p>
<p>Use the discriminant to determine the number of real solutions that each equation has.</p><p><code class='latex inline'>-2x^2+8x-8=0</code></p>
<p>Use the discriminant to determine the number of roots for each quadratic equation.</p><p><code class='latex inline'>3x^2 + 4x + \frac{4}{3}= 0</code></p>
<p>Use the discriminant to determine the number of roots for each quadratic equation.</p><p><code class='latex inline'>2x^2 - 8x + 9= 0</code></p>
<p>Use the discriminant to determine the number of roots for each equation.</p><p><code class='latex inline'>3x^2+ 4x - 5 = 0</code></p>
<p>Use the discriminant to determine the number of roots for each quadratic equation.</p><p><code class='latex inline'>x^2 - 5x +4 = 0</code></p>
<p>A tangent is a line that touches a circle at exactly one point. For what values of <code class='latex inline'>k</code> will the line <code class='latex inline'>y=x+k</code> be tangent to the circle <code class='latex inline'>x^2+y^2=25</code>?</p>
<p>Use the discriminant to determine the number of real solutions that each equation has.</p><p> <code class='latex inline'>-17x-9=4x^2-5x</code></p>
<p>The height, <code class='latex inline'>h(t)</code>, of a projectile, in metres, can be modelled by the equation <code class='latex inline'>h(t) = 14t - 5t^2</code>, where t is the time in seconds after the projectile is released. Can the projectile ever reach a height of 9m? Explain.</p>
<p><strong>(a)</strong> Copy the graph of <code class='latex inline'>f(x) = (x - 2)^2 - 3</code>. Then draw lines with slope -4 that intersect the parabola at </p> <ul> <li>(i) one point,</li> <li>(ii) two points and </li> <li>(iii) no points.</li> </ul> <p><strong>(b)</strong> Write the equations of the lines from part (a).</p><p><strong>(c)</strong> How are all of the lines with slope - 4 that do not intersect the parabola related?</p>
<p>State the number of times that each relation passes through the x-axis. Justify your answer</p><p> <code class='latex inline'>y=3(x+2)^2-5</code></p>
<p>Use the discriminant to determine the number of roots for each equation.</p><p><code class='latex inline'>9x^2 -12x + 4 = 0 </code></p>
<p>State the number of times that each relation passes through the x-axis. Justify your answer</p><p><code class='latex inline'>y=-4.9x^2+5</code></p>
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