Graphing Quadratic Functions in Vertex Form Cheat Sheet

Key Facts

• Vertex form is $y = a(x - h)^2 + k$, where the vertex is $(h, k)$.
• The axis of symmetry for $y = a(x - h)^2 + k$ is the vertical line $x = h$.
• If $a > 0$, the parabola opens upward and the vertex is a minimum point.
• If $a < 0$, the parabola opens downward and the vertex is a maximum point.
• If $|a| > 1$, the parabola is vertically stretched and becomes narrower than $y = x^2$.
• If $0 < |a| < 1$, the parabola is vertically compressed and becomes wider than $y = x^2$.
• The $y$-intercept is found by substituting $x = 0$ into $y = a(x - h)^2 + k$.
• The $x$-intercepts are found by setting $y = 0$ and solving $0 = a(x - h)^2 + k$.

Vocabulary

Quadratic function

A function whose highest power of $x$ is $2$, often forming a U-shaped graph called a parabola.

Vertex form

The form $y = a(x - h)^2 + k$, which shows the vertex and transformations of a quadratic function.

Vertex

The point $(h, k)$ where a parabola changes direction and reaches its maximum or minimum value.

Axis of symmetry

The vertical line $x = h$ that divides the parabola into two matching halves.

Vertical stretch or compression

A change controlled by $|a|$ that makes the parabola narrower when $|a| > 1$ or wider when $0 < |a| < 1$.

Intercept

A point where the graph crosses an axis, such as the $y$-intercept when $x = 0$ or an $x$-intercept when $y = 0$.