How to Graph Quadratic Functions? (+FREE Worksheet!)
Learn how to Graph Quadratic Functions in the vertex or standard forms following a few simple steps.
![How to Graph Quadratic Functions? (+FREE Worksheet!)](https://www.effortlessmath.com/wp-content/uploads/2020/04/Graphing-Quadratic-Functions-Cover-512x240.jpg)
Related Topics
- How to Solve Quadratic Inequalities
- How to Solve a Quadratic Equation
- How to Graph Quadratic Inequalities
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 \(y\).
A Perfect Practice Workbook for Algebra I
Graphing Quadratic Functions – 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.
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/u.png)
Graphing Quadratic Functions – Example 2:
Sketch the graph of \(y=3(x+1)^2+2\).
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 \(y=3(x+1)^2+2\) 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.
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/h.png)
Exercises for Graphing Quadratic Functions
Best Algebra Prep Resource
Sketch the graph of each function. Identify the vertex and axis of symmetry.
- \(\color{blue}{y = 3(x-5)^2-2}\)
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/gg.png)
- \(\color{blue}{y=x^2-3x+15}\)
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/gg-1.png)
Download Graphing Quadratic Functions Worksheet
![](https://www.effortlessmath.com/wp-content/uploads/2019/12/answers.png)
- \(\color{blue}{y = 3(x-5)^2-2}\)
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/3-4.png)
- \(\color{blue}{y=x^2-3x+15}\)
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/4-4.png)
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