Question

Consider the following graph of a quadratic function. Write the equation for the quadratic function in standard form.

Answer 1

y=x^2+6x+7
or
x^2 +6x+7=y

Answer 2

`f(x)=x^2+6x+7`

Explanation:

The vertex form of a parabola is

`f(x)=a(x-h)^2+k` .... (1)

where, a is a constant, (h,k) is vertex of the parabola.

From the given graph it is clear that the vertex of the parabola is (-3,-2).

Substitute h=-3 and k=-2 in equation (1).

`f(x)=a(x-(-3))^2+(-2)`

`f(x)=a(x+3)^2-2` .... (2)

The graph is passes through the point (-2,-1). So, the function must be satisfy by the point (-2,-1).

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

`-1=a-2`

Add 2 on both sides.

`-1+2=a-2+2`

`1=a`

The value of a is 1. Substitute this value in equation (2).

`f(x)=(1)(x+3)^2-2`

`f(x)=(x+3)^2-2`

`f(x)=x^2+6x+9-2`

`f(x)=x^2+6x+7`

Therefore, the standard form of the parabola is
`f(x)=x^2+6x+7`.