Unit 6 Review: Quadratic Functions

Which expression is the complete factorization of 45 - 5y^2?

(Hint: use the calculator to reduce the answers to two possible choices, then choose the answer that is more factored.)

• 5(9-y^2)

• 5(3-y)^2

• 5(y+3)(y-3)

• 5(3-y)(3+y)

What are the reasonable domain and range of the quadratic function f(x)=0.25(x+6)(x-2)?

(Hint: use your graphing calculator or https://www.desmos.com/testing/texas/graphing)

• Domain: -6 ≤ x ≤ 2

  Range: -4 ≤ f(x) ≤ 0

• Domain: All real numbers

  Range: All Real Numbers

• Domain: All real numbers

  Range: f(x) ≥ -4

• Domain: x ≥ -6

  Range: f(x) ≥ -4

Which of the following represents the domain of the quadratic function f(x) = x^2 - 5?

• The set of positive real numbers.

• The set of real numbers greater than or equal to -5.

• The set of all real numbers.

• The set of real numbers less than or equal to -5.

What are the solutions to the equation

3x^2 = 30x + 72?

Select TWO correct answers.

(Hint: move everything to the same side of the = sign and graph. Look for the x-intercepts)

• x = -2

• x = 2

• x = 12

• x = -12

What values of n make the equation

2n^2 + 15 = -11n true?

Select TWO correct answers.

• -5

• -3

• -2.5

• 2.5

• 3

Which is the range of the relation y=-x^2 - 2x if the domain is the set {-3, -2, -1}?

(Hint: put the equation in the calculator then push 2nd graph and look at the y values for the given x-values).

• {0, -3, -8}

• {0, 1, 3}

• {-3, 0 1}

• {-15, -8, -3}

The table shows the population of a town from 1996 to 2004. Assume that t is the number of years since 1996 and P is measured in thousands of people.

Use the quadratic regression equation to predict the population in the year 2007. Round to the nearest whole number.

The quadratic equation y= -x^2 - 3x + 4 is graphed below.

What are the zeros of the related function f(x) = -x^2 - 3x + 4?

Hint: the zeros are the x-intercepts.

• -3 and 4

• -4 and 1

• 0 and 4

• -3 and -4

If g(x) = (x - a)(x - b) where both a and b represent real numbers, which statement is true?

• The zeros of the function is f(0).

• The zeros of the function are x = a and x = b.

• The zeros of the function are f(-a) and f(-b).

• The zeros of the function are x = -a and x = -b.

Given f(x) = x^2 - 81, which statement is true?

• The only zero, 9, can be found when 0 = (x - 9)(x - 9).

• The only zero, 27, can be found when 0 = (x - 27)(x - 27)

• The zeros, -9 and 9, can be found when 0 = (x + 9)(x - 9)

• The zeros, -27 and 27, can be found when 0 = (x + 27)(x - 27).