Question

The quadratic function f(x) has roots of -4 and 2 and point (1, -5) lles on f(x). What is the equation of f(x)?

Of(x) = (x-2)(x+4)
Of(x) = (x-2)(x-4)
Of(x) = 4(x-2)(x+4)
Of(x) = 4(x-2)(x-4)

I need help with both please

Answer 1

Answer: first option f(x)=(x-2)(x+4)

Roots are the zeros of the quadratic function, meaning they are the x-values that produce an output of 0. So, to cancel out numbers to equal zero, you must use inverse properties. If x=-4, then (-4+4)=0, and if x=2, then (2-2)=0, which means (x-2)(x+4) is the correct expanded quadratic equation.

Now, let’s determine if (1, -5) is a solution to this equation.

When x=1, f(x)=?

f(x)=((1)-2)((1)+4)

f(x)=(-1)(5)

f(x)=-5

So, when x=1, f(x), or y, = -5, meaning (1, -5) is a solution to the quadratic.