Integrated Math 2 / Unit 3: Quadratic Functions
3.4 Standard Form to Vertex Form
Notes
Use the axis formula to find the vertex from standard form, then write vertex form.
- Step 1: $\displaystyle h = -\frac{b}{2a}$.
- Step 2: $k = f(h)$.
- Step 3: write $y = a(x - h)^2 + k$, keeping the same $a$.
- Example: $y = x^2 + 6x + 5$ gives $h = -3$, $k = 9 - 18 + 5 = -4$, so $y = (x + 3)^2 - 4$.
Practice
Find the vertex of $y = x^2 + 6x + 5$.
$\displaystyle h = -\frac{6}{2} = -3$ and $k = 9 - 18 + 5 = -4$.
Write $y = 2x^2 - 8x + 3$ in vertex form.
$\displaystyle h = \frac{8}{4} = 2$ and $k = 8 - 16 + 3 = -5$. Keep $a = 2$.
What is the maximum value of $y = -x^2 + 4x - 1$?
$h = 2$ and $k = -4 + 8 - 1 = 3$. The parabola opens down, so 3 is the maximum.
Ready for more? Take the Unit 3 test.