(21E+) 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".