Question 1

Given the quadratic function $$f(x) = -2x^2$ + 4x + 2$$, what are the coordinates of the vertex?

Accepted Answer

$$(1, 4)$$

Question 2

Which of the following statements is TRUE about the graph of $$f(x) = ax^2$ + bx + c if$$ $$a \u003c 0$$?

Accepted Answer

The vertex is the highest point and the parabola opens down.

Question 3

For the quadratic function $$f(x) = 3(x-1)^2$ + 2$$, what transformation has been applied to the parent function $$y = x^2$?

Accepted Answer

Shift right 1 unit, stretch vertically by 3, shift up 2 units.

Question 4

What is the axis of symmetry for the quadratic function $$f(x) = x^2$ - 4x + 4$$?

Accepted Answer

$$x = 2$$

Question 5

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 reached by the ball?

Accepted Answer

$$22$$ meters

Question 6

If the discriminant $$b^2 - 4ac$ of a quadratic function is negative, what does this indicate about the graph?

Accepted Answer

The graph does not intersect the x-axis.

Question 7

Given $$f(x) = x^2$ - 4x + 4$$, what is the range of $$f$$?

Accepted Answer

$$[0, \infty)$$

Question 8

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

Accepted Answer

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

Question 9

A company models its profit with $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$18 at$$ $$x = 2$$ thousand units.

Question 10

Which of the following quadratic functions has its vertex at $$(1, 2)$$?

Accepted Answer

$$f(x) = 3(x-1)^2$ + 2$$

Question 11

If a parabola opens up and its vertex is at $$(2, -3)$$, which of the following could be its equation?

Accepted Answer

$$f(x) = a(x-2)^2$ - 3$$, where $$a \u003e 0$$

Question 12

Which of the following best describes the effect of the coefficient $$a in$$ $$f(x) = a(x-h)^2$ + k$$?

Accepted Answer

It determines whether the parabola opens up or down and the vertical stretch or compression.

Question 13

Given $$f(x) = x^2$ + 2x + 5$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$4$$

Question 14

A satellite dish is shaped like a parabola described by $$y = 0.5(x-3)^2$ + 2. $$What is the lowest point on the dish?

Accepted Answer

$$(3, 2)$$

Question 15

If $$f(x) = -x^2$ + 6x - 8$$, for which interval is $$f(x)$$ increasing?

Accepted Answer

$$(-\infty, 3)$$

Question 16

Which of the following real-world scenarios can be modeled by a quadratic function?

Accepted Answer

The height of a projectile over time.

Question 17

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

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 18

If the vertex of a parabola is at $$(h, k)$$ and the parabola opens down, which of the following statements is correct?

Accepted Answer

The maximum value of the function is $$k.$$

Question 19

A quadratic function has no real x-intercepts. Which of the following must be true?

Accepted Answer

$$b^2 - 4ac$$ \u003c 0$$

Properties and Graphing of Quadratic Functions

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