Lining Up Quadratics

Learning Focus

Match quadratic equations to graphs by using vertex, direction, intercepts, and points.

Big idea

Checklist:

1. Direction (sign of $a$).
2. Vertex $(h,k)$ and axis $x=h$.
3. $y$-intercept (set $x=0$).
4. $x$-intercepts (set $y=0$): none, one, or two.

Worked example

Vertex $(2,-3)$, opens up: $y=(x-2)^2-3$. Its $x$-intercepts: $(x-2)^2=3$, so $x=2\pm\sqrt3$, two intercepts. $y$-intercept: $4-3=1$.

Takeaways

• Use the vertex first, then one more point to find $a$.
• An upward parabola with vertex below the $x$-axis has two $x$-intercepts.
• Verify a match by testing a point.