Checkpoint: Writing Quadratic Equations in Vertex Form to Graph Solution

Write the quadratic equation in vertex form. Name the vertex and axis of symmetry.

$x = 4 y^{2} - 8 y - 5$

$\begin{array}{rcl} 4 y^{2} - 8 y - 5 & = & 0 \\ 4 y^{2} - 8 y & = & 5 \\ 4 (y^{2} - 2 y) & = & 5 \\ 4 (y^{2} - 2 y + {(\frac{2}{2})}^{2}) & = & 5 + 4 {(\frac{2}{2})}^{2} \\ 4 {(y - 1)}^{2} & = & 5 + 4 (1) \\ 4 {(y - 1)}^{2} & = & 9 \\ 4 {(y - 1)}^{2} - 9 & = & 0 \\ x & = & 4 {(y - 1)}^{2} - 9 \end{array}$

The vertex is $(- 9, 1) .$ The axis of symmetry is $y = 1 .$

Note

Q: What direction will the parabola open? Explain.

A: The parabola will open right because $a = 4$ and the equation is $x = y^{2} .$