Graphing Quadratic Equations

Standard Form of a Quadratic Function

The standard form of a quadratic function is expressed as $y = ax^2 + bx + c$. In this form,

• $a$ determines the direction of the parabola (upward if $a > 0$, downward if $a < 0$).

• $b$ and $c$ influence the position and shape of the parabola.

The value of $c$ represents the y-intercept of the graph.

Vertex Form of a Quadratic Function

The vertex form of a quadratic function is expressed as $y = a(x-h)^2 + k$. In this form,

• $a$ determines the direction and the width of the parabola.

• $(h, k)$ is the vertex of the parabola where it turns.

This form is useful for quickly identifying the vertex and graphing the function.

Factored Form of a Quadratic Function

The intercept form of a quadratic function is expressed as $y = a(x-p)(x-q)$. In this form,

• $p$ and $q$ are the x-intercepts of the parabola.

• The graph crosses the x-axis at these intercepts.

This form is useful for easily finding the x-intercepts and sketching the graph.

Think about the 3 different forms for graphing and answer the following questions.