Question

Find the standard form the equation of the parabola with the vertex (2,-3), a vertical axis and passing through the point (4,0)

Answer 1

do you know the vertex form of a parabola?

Answer 2

y=a(x-h)^2+k

Answer 3

\(\bf vertex\ ({\color{red}{ 2}},{\color{blue}{ -3}})\implies y={\color{green}{ a}}(x-{\color{red}{ 2}})^2+({\color{blue}{ -3}})\implies y={\color{green}{ a}}(x-2)^2-3
\\ \quad \\
\textit{we know that it passes through }(4,0)\quad thus
\\ \quad \\
x=4\qquad y=0\implies 0={\color{green}{ a}}(4-2)^2-3\)

just solve for "a" to get that factor

Answer 4

thank you!

Answer 5

yw