Question

4.Which of the following are most likely factors of the function graphed above?

A. (x+1)(x-5)
B. (x)(x-5)
C. (x-1)(x+5)
D. (x)(x+5)

5.What is the solution to the following equation?
x^2-10x+24=0
A. x=3 or x=8
B. x=-3 or x=-8
C. x=4 or x=6
D. x=-4 or x=-6

Answer 1

the equation of the graph is represented by a parabola:

(x + 2)^2 = y +9

Simplify

X^2 + 4x + 4 = y +9

Y = x^2 + 4x + 4 – 9

Y = x^2 + 4x -5

Y = (x+5) ( x -1)

5. x^2 – 10x + 24 = 0

(x -6) ( x - 4) =0

X = 6

X = 4

Answer 2

4)

In the graph we can see that the graph intersects the x axis at -5 & 1

So x = -5 or x= 1

Hence

x +5 = 0 or x -1 = 0

Multiplying them we get

(x+5)(x-1) are the correct factors

Option C) is the right answer

5)

We have

x² - 10x + 24=0

We need two numbers which add to give -10 & multiply to give 24.

The numbers are -6 & -4

We split the term -10x

We get

x² -6x-4x+24=0

x(x-6)-4(x-6)=0

(x-6)(x-4)=0

Using Zero Product rule

x-6 = 0 or x-4=0

x = 6 or x = 4

Option C) is the right answer.