Question

Write a polynomial function whose graph
has (−4, 0), (−3, 0) as x-intercepts and has
a leading coefficient of 4.

Answer 1

\[f(x)=4(x+4)(x+3)\]

Answer 2

@Jonask Please explain how did you get this?

Answer 3

the polynomial with two roots (x-intercept) is a parabola
with equation
\[y=ax ^{2}+bx+c\]
these can also be written in intercept form \[y=a(x-x _{1})(x-x _{2})=a(x-4)(x-3)\]
since \[x=-4,x=-3\] are our zeros(factors)
but we know the coefficient of \[x ^{2}\] is 4
so \[a=4\]
\[y=4(x-4)(x-3)\]
these can be expanded \[y=4(x ^{2}-7x+12)\]
\[y=4x ^{2}-28x+48\]