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Factored Form $f\left(x\right)=a\left(x-p\right)^2$

Graph the following functions on the grid above.

$f\left(x\right)=\left(x-3\right)^{2}$

$g\left(x\right)=-3\left(x+1\right)^{2}$

$h\left(x\right)=\frac{1}{4}\left(x+4\right)^{2}$

Write down the coordinates of the

$x$ -intercept.

$f\left(x\right)$

$g\left(x\right)$

$h\left(x\right)$

Write down the coordinates of the $y$ -intercept for each function.

$f\left(x\right)$

$g\left(x\right)$

$h\left(x\right)$

Write down the equation of the axis of symmetry for each function.

$f\left(x\right)$

$g\left(x\right)$

$h\left(x\right)$

Write down the coordinates of the vertex for each function.

$f\left(x\right)$

$g\left(x\right)$

$h\left(x\right)$

[Practice] For the function $f\left(x\right)=\frac{1}{2}\left(x-1\right)^2$ , find:

the coordinates of the

$x$ -intercept.

the coordinates of the

$y$ -intercept.

the equation of the axis of symmetry.

the coordinates of the vertex.

the concavity of the parabola. Write "concave up" or "concave down".

[Practice] For the function $f\left(x\right)=-x^2-10x-25$ , find:

it in the form

$-\left(x-p\right)^2\qquad f\left(x\right)=$

the coordinates of the

$x$ -intercept.

the coordinates of the

$y$ -intercept.

the equation of the axis of symmetry.

the coordinates of the vertex.

the concavity of the parabola. Write "concave up" or "concave down".

[Practice] For the function $f\left(x\right)=4x^2-4x+1$ , find:

it in the form

$4\left(x-p\right)^2\qquad f\left(x\right)=$

the coordinates of the

$x$ -intercept.

The coordinates of the

$y$ -intercept.

The equation of the axis of symmetry.

The coordinates of the vertex.

The concavity of the parabola. Write "concave up" or "concave down".

BackFactored Form f(x)=a(x−p)2f\left(x\right)=a\left(x-p\right)^2

Factored Form $f\left(x\right)=a\left(x-p\right)^2$