Question 1

Which of the following is the vertex form of a quadratic function?

Accepted Answer

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

Question 2

Given the quadratic function $$f(x) = -2(x + 3)^2$ + 5$$, what is the vertex of the parabola?

Accepted Answer

$$(-3, 5)$$

Question 3

For the function $$f(x) = 3x^2$ - 12x + 7$$, what is the axis of symmetry?

Accepted Answer

$$x = 2$$

Question 4

A quadratic function models the height (in meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 19.6t + 2. $$What is the maximum height the ball reaches?

Accepted Answer

$$21.6$$ meters

Question 5

Which transformation occurs to the graph of $$f(x) = x^2$ to obtain g(x) = (x$$ - $$4)^2 + 2$?

Accepted Answer

Shift right 4 units and up 2 units

Question 6

If a parabola opens downward and has its vertex at $$(1, 7)$$, which of the following could be its equation?

Accepted Answer

$$f(x) = -2(x - 1)^2$ + 7$$

Question 7

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

Accepted Answer

$$(2, 0)$$ and $$(4, 0)$$

Question 8

Which of the following best describes the domain and range of $$f(x) = -x^2$ + 3$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(-\infty, 3]$$

Question 9

A quadratic function in standard form is $$f(x) = ax^2$ + bx + c. $$What is the formula for the $$x-$$coordinate of the vertex?

Accepted Answer

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

Question 10

Which method is most appropriate for solving $$x^2 - 9 = 0$?

Accepted Answer

Square root property

Question 11

If $$f(x) = 2(x + 1)^2$ - 4$$, what is $$f(0)$$?

Accepted Answer

$$-2$$

Question 12

A parabola has its vertex at $$(2, -3)$$ and passes through the point $$(3, 1). If $$its equation is $$f(x) = a(x - 2)^2$ - 3$$, what is the value of $$a$$?

Accepted Answer

$$4$$

Question 13

Which of the following statements is true about the graph of $$f(x) = -x^2$ + 4x - 1$$?

Accepted Answer

It opens downward and has a maximum value.

Question 14

Given $$f(x) = (x - 2)^2$ + 1$$, for which values of $$x is $$the function increasing?

Accepted Answer

$$x \u003e 2$$

Question 15

Which of the following is the correct process to convert $$f(x) = x^2$ + 8x + 5 to $$vertex form?

Accepted Answer

Complete the square: $$f(x) = (x + 4)^2$ - 11$$

Question 16

A real-world scenario: The profit $$P(x) (in $$dollars) from selling $$x$$ units of a product is modeled by $$P(x) = -5x^2$ + 200x - 1000. $$How many units should be sold to maximize profit?

Accepted Answer

$$x = 20$$

Question 17

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

Accepted Answer

If $$|a| \u003e 1$$, the parabola is narrower; if $$0 \u003c |a| \u003c 1$$, it is wider.

Question 18

Given $$f(x) = -3(x + 2)^2$ + 4$$, what is the range of the function?

Accepted Answer

$$(-\infty, 4]$$

Question 19

If $$f(x) = (x - 1)^2$ - 9$$, what is the $$y-$$intercept of the function?

Accepted Answer

$$-8$$

Quadratic Functions: Properties, Vertex Form, and Transformations

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