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".