Question

When you don’t know the value of a! Follow these steps attached below! Write a quadratic in vertex form whose graph has the given vertex (1,2) and passes through (3,10)

Answer 1

The vertex form of a quadratic equation is:

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

The given vertex is (1,2)

It follows h = 1, k = 2

Substitute the values into the vertex equation

`y=a(x-1)+2`

Since the line passes through (3,10) substitute x=3 and y=10 into the equation

This gives

`10=a(3-1)^2+2`

Solve for a

`\begin{gathered} 10=a(2)^2+2 \\ 10=4a+2 \\ 8=4a \\ a=2 \end{gathered}`

Substitute the value of a into the vertex form equation

`y=2(x-1)^2+2`

The required equation is:

`y=2(x-1)^(2)+2`