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Vertex Form $f\left(x\right)=\left(x-h\right)^2+k$


Graph the following functions on the grid above.
$f\left(x\right)=x^2$
$g\left(x\right)=x^2+1$
$h\left(x\right)=x^2+3$
$j\left(x\right)=x^2-2$
Write down the coordinates of the vertex and equation fo the axis of symmetry for each function.

vertex:

vertex:

vertex:

vertex:

axis of symmetry:

axis of symmetry:

axis of symmetry:

axis of symmetry:

Graph the following functions on the grid above.
$p\left(x\right)=x^2$
$q\left(x\right)=\left(x+1\right)^2$
$r\left(x\right)=\left(x+3\right)^2$
$s\left(x\right)=\left(x-2\right)^2$
Write down the coordinates of the vertex and equation fo the axis of symmetry for each function.

vertex:

vertex:

vertex:

vertex:

axis of symmetry:

axis of symmetry:

axis of symmetry:

axis of symmetry:

Graph the following functions on the grid above.
$t\left(x\right)=\left(x+1\right)^2+3$
$u\left(x\right)=\left(x+3\right)^2-5$
$v\left(x\right)=\left(x-2\right)^2+4$
$w\left(x\right)=\left(x-6\right)^2-1$
Write down the coordinates of the vertex and equation fo the axis of symmetry for each function.

vertex:

vertex:

vertex:

vertex:

axis of symmetry:

axis of symmetry:

axis of symmetry:

axis of symmetry:
Consider the following quadratic functions.
$f\left(x\right)=\left(x+2\right)^{2}-1$
$g\left(x\right)=-\left(x-3\right)^{2}+5$
$h\left(x\right)=-\left(x-2\right)^{2}$

Vertex

Write down the coordinates of the vertex for each function.

vertex:

vertex:

vertex:

Axis of Symmetry

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

$f\left(x\right)$

$g\left(x\right)$

$h\left(x\right)$

$y$-intercept

To find the $y$-intercept of a function, we substitute $x=$

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

$f\left(x\right)$

$g\left(x\right)$

$h\left(x\right)$

Concavity

Describe the concavity of the parabola for each function. Write “concave up” or “concave down”.

$f\left(x\right)$

$g\left(x\right)$

$h\left(x\right)$

[Example] For the function $f\left(x\right)=-\left(x+3\right)^{2}+6$, find:

the coordinates of the vertex.

the equation of the axis of symmetry.

the coordinates of the $y$-intercept.

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

[Example] For the function $f\left(x\right)=\left(x-\frac{1}{2}\right)^{2}-\frac{1}{4}$, find:

the coordinates of the vertex.

the equation of the axis of symmetry.

the coordinates of the $y$-intercept.

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