Question

write a quadratic function in standard form whose graph passes through (-6,0)(-4,0)(-3,-18) f(x)= [answer]​

Answer 1

Using the Factor Theorem, the quadratic equation is given by:

$f(x) = 6(x^2 + 10x + 24)$

What is the Factor Theorem?

The Factor Theorem states that a polynomial function with roots $x_1, x_2, \codts, x_n$ is given by:

$f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)$

In which a is the leading coefficient.

In this problem, we have a quadratic function, meaning that it has two roots, and it passes through (-6,0) and (-4,0), hence the roots are $x_1 = -4, x_2 = -6$, thus:

$f(x) = a(x + 4)(x + 6)$

$f(x) = a(x^2 + 10x + 24)$

Considering that it passes through (-3, -18), we can find a, hence:

$18 = a[(-3)^2 + 10(-3) + 24]$

$3a = 18$

$a = 6$

Hence the equation is:

$f(x) = 6(x^2 + 10x + 24)$

More can be learned about the Factor Theorem at https://brainly.com/question/24380382