Question 1

Which of the following equations represents a quadratic function in standard form?

Accepted Answer

$$f(x) = a(x-h)^2$ + k$$

Question 2

Given the quadratic function $$f(x) = 2x^2$ - 8x + 3$$, what are the coordinates of the vertex?

Accepted Answer

$$(2, -5)$$

Question 3

A company models its profit with the function $$P(x) = -3x^2$ + 12x + 5$$, where $$x is $$the number of units sold. What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $$23 at$$ $$x = 2$$ units

Question 4

Which transformation occurs when the quadratic function $$f(x) = x^2$ is changed to f(x$$) = $$-2(x-3)^2 + 4$?

Accepted Answer

Reflected over the x-axis, stretched by a factor of 2, shifted right 3 units and up 4 units

Question 5

If a quadratic function opens downward, which of the following must be true about its leading coefficient $$a$$?

Accepted Answer

$$a \u003c 0$$

Question 6

Given $$f(x) = x^2$ + 6x + 8$$, what are the x-intercepts of the graph?

Accepted Answer

$$x = -4$$ and $$x = -2$$

Question 7

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h(t) = -5t^2$ + 20t + 2. $$What is the maximum height the ball reaches?

Accepted Answer

$$22$$ meters at $$t = 2$$ seconds

Question 8

Which of the following describes the effect of the transformation $$f(x) = (x+5)^2$ - 7 on $$the parent function $$f(x) = x^2$?

Accepted Answer

Shift left 5 units and down 7 units

Question 9

If the vertex of a parabola is at $$(3, -2)$$ and the parabola opens upward, which equation could represent this parabola?

Accepted Answer

$$f(x) = (x-3)^2$ - 2$$

Question 10

Given the quadratic function $$f(x) = -x^2$ + 4x - 1$$, what is the y-intercept?

Accepted Answer

$$(0, -1)$$

Question 11

A satellite dish is shaped like a parabola described by $$y = 0.5x^2$. If the dish is 4 meters wide, what is the depth at the center (x = 0$)?

Accepted Answer

$$0$$ meters

Question 12

Which of the following is NOT a property of all parabolas?

Accepted Answer

They always open upward

Question 13

For the quadratic function $$f(x) = 3(x+2)^2$ - 5$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$-5$$

Question 14

Which method is most appropriate for finding the x-intercepts of a quadratic function in standard form $$f(x) = a(x-h)^2$ + k$$?

Accepted Answer

Square root method

Question 15

If $$f(x) = -2x^2$ + 8x - 3$$, what is the axis of symmetry?

Accepted Answer

$$x = 2$$

Question 16

A bridge is designed in the shape of a parabola with equation $$y = -0.25x^2$ + 4. $$What is the maximum height of the bridge?

Accepted Answer

$$4$$ units

Question 17

Which of the following statements is true about the graph of $$f(x) = 5x^2$ + 2x + 1$$?

Accepted Answer

It opens upward and has a minimum point

Question 18

If $$f(x) = a(x-h)^2$ + k$$ and $$a is $$multiplied by a number greater than 1, what happens to the graph?

Accepted Answer

It becomes narrower (stretched vertically)

Question 19

A projectile is launched and its height is modeled by $$h(t) = -16t^2$ + 32t + 10. At $$what time does it reach its maximum height?

Accepted Answer

$$t = 1$$ second

Question 20

Which of the following is the correct formula for the vertex $$x-$$coordinate of a quadratic function in general form $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

$$x = -\frac{b}{2a}$$

Quadratic Functions: Structure, Properties, and Graphing

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