Question

For the following problem find the quadratic function y=f(x) that has the given vertex and whose graph passes through the given point. Write the function in standard form.Vertex (1,2) passing through (2,5)

Answer 1

Given: vertex (1,2) passing through (2,5).

Find: quadratic function.

Explanation: the vertex form of equation is

$f(x)=a(x-h)^2\text{ +k }$

where( h,k) represents the vertex so on putting the value of x =2 and f(x)=5, we get

$\begin{gathered} 5=a(2-1)^2+2 \\ a=3 \end{gathered}$

hence the quadratic function is

$\begin{gathered} f(x)=3(x-1)^2+2 \\ =3(x^2+1-2x)+2 \\ =3x^2+3-6x+2 \\ =3x^2-6x+5 \end{gathered}$

Final answer: the quadratic function is

$f(x)=3x^2-6x+5$