State the domain and range of each relation.
State the domain and range of each relation.
State the domain and range of each relation.
{(1, 4), (2, 6), (3, 10), (4, 18), (5, 29)}
State the domain and range of each relation.
y = 2x^2 + 11
Which relations below is a function? Justify your answers.
{(1, 4), (2, 6), (3, 10), (4, 18), (5, 29)}y = 2x^2 + 11
A linear function machine produces the points (2, 5) and (-3, -15).
Determine the equation of the function.
A linear function machine produces the points (2, 5) and (-3, -15).
Is it possible for there to be more than one function to exist that will generate these values? Explain.
(a) Draw a mapping diagram for these data:
{(4, -2), ((6, 1), (11, -7), (6, 7), (4, -7)}
(b) Is this relation a function? Explain.
A hall charges $30 per person for a sports banquet when 120 people attend. For every 10 extra people that attend, the hall will decrease the price by $1.50 per person. What number of people will maximize the revenue for the hall?
The power, P, in watts, produces by a solar panel is given by the function P(I) = -5I^2 + 100I, where I represents the current, in amperes (A).
(a) What value of the current will maximize the power?
(b) What is the maximum power?
Perform each radical operation and simplify where needed.
\sqrt{27} -4\sqrt{3}+ \sqrt{243} - 8\sqrt{81} + 2
Perform each radical operation and simplify where needed.
-3\sqrt{3}(\sqrt{3}+ 5\sqrt{2})
Perform each radical operation and simplify where needed.
(\sqrt{3}+5)(5 - \sqrt{3})
Perform each radical operation and simplify where needed.
5\sqrt{2}(11 + 2\sqrt{2})-4(8 + 3\sqrt{2})
Find a simplified expression for the area of each shape.
Find a simplified expression for the area of each shape.
Solve each quadratic equation. Give exact answers.
3x^2 -2x - 2=0
Solve each quadratic equation. Give exact answers.
6x^2 -23x + 20 = 0
Use the discriminant to determine the number of roots for each equation.
3x^2+ 4x - 5 = 0
Use the discriminant to determine the number of roots for each equation.
-2x^2+ 5x - 1= 0
Use the discriminant to determine the number of roots for each equation.
9x^2 -12x + 4 = 0
Jessica reasoned that since 2 \times 2 =4 and 2 + 2 = 4, \sqrt{2} + \sqrt{2} must have the same value as \sqrt{2} \times \sqrt{2}. Is she correct? Justify your answer.
Determine the equation in standard form for each quadratic function.
x-intercepts -2 and 5, containing the point (3, 5)
Determine the equation in standard form for each quadratic function.
x-intercepts -2 \pm \sqrt{5}, containing the point (-4, 5).
A golf ball is hit, and it lands at a point on the same horizontal plane 53 m away. The path of the ball took it just over a 9m tall tree that was 8m in front of the golfer.
(a) Assume the ball is hit from the origin of a coordinate plane. Find a quartic function that describes the path of the ball.
(b) What is the maximum height of the ball?
(c) Is possible to move the origin in this situation on and develop another quadratic function to describe the path? If so, find a second quartic function.
Determine the points of intersection of each pair of functions.
y = 4x^2 - 15x + 20 and y = 5x - 4
Determine the points of intersection of each pair of functions.
y = -2x^2 + 9x + 9 and y = -3x - 5
For what value of b will the line y = -2x + b be tangent to the parabola y = 3x^2 + 4x - 1?
Do all linear-quadratic systems result in a solution? Justify your answer using examples.