Question

Write an equation for a polynomial with all the following features: The degree is 5, the polynomial has 4 terms and the graph of the polynomial crosses the vertical axis at y=12

Answer 1

we must apply the formula

$y=x^2+bx\times c$$3.25x^5+4x^{4^{}}\text{ }+5.5x^{3\text{ }}+x^2$

now we apply the formula to find x,

$\begin{gathered} h=\frac{b}{2(a)} \\ h=\frac{-4}{2(1)} \\ h=-2 \end{gathered}$

having already x now we apply the formula to find the vertex at y that intersects at point 12.

$\begin{gathered} f(-2)=3.25(-2)^{5\text{ }}+4(-2)^{4^{}}+5.5(-2)^{3^{}}\text{ }+(-2)^{2^{}} \\ f(-2)=104-64-44-8 \\ =-12 \end{gathered}$