Question

1. select the correct factored form for the following quadratic expression

$x^2 - 2x - 63$

a) $(x - 7)(x - 9)$

b) $(x + 7)(x + 9)$

c) $(x + 7)(x - 9)$

d) $(x - 7)(x + 9)$

1. select the ordered pair below that is the vertex of the function

$f(x) = x^2 + 8x + 15$

a) $(-4, 1)$

b) $(4, 53)$

c) $(-8, 15)$

d) $(-4, -1)$

1. multiply the following functions, and select the correct product

$f(x) = x - 8$ and $g(x) = x + 8$

a) $f cdot g = x^2 + 16x + 64$

b) $f cdot g = x^2 - 16x - 64$

c) $f cdot g = x^2 + 64$

d) $f cdot g = x^2 - 64$

1. select the inverse of the function $y = 5x - 1$

a) $y = 5x - 1$

b) $y = \frac{x + 1}{5}$

c) $y = -1 + 5x$

d) $y = \frac{x - 1}{5}$

1. select the appropriate solutions for the factored equation $0 = (2x + 7)(4x - 3)$.

a) $x = \frac{7}{2}$ & $x = \frac{1}{4}$

b) $x = 7$ & $x = 2$

c) $x = 7$ & $x = -3$

d) $x = -\frac{7}{2}$ & $x = \frac{3}{4}$

Explanation:

Question 4

Step1: Find two numbers

Find two numbers that multiply to -63 and add to -2. The numbers are -9 and 7.

Step2: Factor the quadratic

Using the numbers, the factored form is \((r + 7)(r - 9)\).

Step1: Find the x - coordinate of the vertex

For a quadratic function \(f(x)=ax^{2}+bx + c\), the x - coordinate of the vertex is \(x=-\frac{b}{2a}\). For \(f(x)=x^{2}+8x + 15\), \(a = 1\), \(b = 8\), so \(x=-\frac{8}{2\times1}=-4\).

Step2: Find the y - coordinate

Substitute \(x=-4\) into \(f(x)\): \(f(-4)=(-4)^{2}+8\times(-4)+15=16-32 + 15=-1\). So the vertex is \((-4,-1)\).

Step1: Use the difference of squares formula

The product of \(f(x)=x - 8\) and \(g(x)=x + 8\) is \((x - 8)(x + 8)\). By the difference of squares formula \((a - b)(a + b)=a^{2}-b^{2}\), here \(a=x\), \(b = 8\), so the product is \(x^{2}-64\).

Answer:

c) \((r + 7)(r - 9)\)

Question 5