Learn how to graph a Quadratic Functions in the vertex or standard forms following few simple steps.

## Step by step guide to Graphing Quadratic Functions

• Quadratic functions in vertex form: $$y=a(x – h)^2+k$$ where $$(h,k)$$ is the vertex of the function. The axis of symmetry is $$x=h$$
• Quadratic functions in standard form: $$y=ax^2+bx+c$$ where $$x=-\frac{b}{2a}$$ is the value of $$x$$ in the vertex of the function.
• To graph a quadratic function, first find the vertex, then substitute some values for $$x$$ and solve for $$y$$.

### Example 1:

Sketch the graph of $$y=(x+1)^2-2$$.

Solution:

First, recall that a Quadratic function in vertex form is $$y=a(x – h)^2+k$$ where $$(h,k)$$ is the vertex of the function. The vertex of $$y=(x+1)^2-2$$ is $$(-1,-2)$$. Substitute zero for $$x$$ and solve for $$y$$. $$y=(0+1)^2-2=-1$$. The $$y$$ Intercept is $$(0,-1)$$.
Now, you can simply graph the quadratic function.

### Example 2:

Sketch the graph of $$y=3(x+1)^2+2$$.

Solution:

The vertex of $$3(x+1)^2+2$$ is $$(-1,2)$$. Substitute zero for $$x$$ and solve for $$y$$. $$y=3(0+1)^2+2=5$$. The $$y$$ Intercept is $$(0,5)$$.
Now, you can simply graph the quadratic function.

## Exercises

### Sketch the graph of each function. Identify the vertex and axis of symmetry.

• $$\color{blue}{y = 3(x-5)^2-2}$$
• $$\color{blue}{y=x^2-3x+15}$$

• $$\color{blue}{y = 3(x-5)^2-2}$$
• $$\color{blue}{y=x^2-3x+15}$$