Question

What are the factors of the quadratic function represented by this graph?OA (x-1) and (x-5)OB (x-1) and (x+5)OC(x-1) and (x+5)OD.(x+1) and (x-5)

Answer 1

ANSWER :

The answer is B. (-x - 1) and (x + 5)

EXPLANATION :

The factors of the quadratic function represent the x-intercepts.

(x-a)(x-b) where the x-intercepts are x = a and x = b

From the graph, the intercepts are x = -5 and x = -1

Then we will write them in the form x - a = 0 and x - b = 0

That will be :

$\begin{gathered} x=-5 \\ \text{ Add 5 to both sides :} \\ x+5=-5+5 \\ x+5=0 \\ \\ \\ x=-1 \\ \text{ Add 1 to both sides :} \\ x+1=-1+1 \\ x+1=0 \end{gathered}$

The factors are (x + 5) and (x + 1)

We can rewrite the quadratic functions as :

$f(x)=a(x+5)(x+1)$

Note that we need to determine the sign of a,

a is positive if the graph opens upward

a is negative if the graph opens downward

Since the graph opens downward, the sign of a must be negative.

Then the equation will be :

$f(x)=-a(x+5)(x+1)$

If we will distribute the negative sign to one of the factors :

This will be :

$\begin{gathered} f(x)=a(-x-5)(x+1) \\ or \\ f(x)=a(x+5)(-x-1) \end{gathered}$

Any of these are correct.

Looking at the choices, we have (-x - 1) and (x + 5)