How to Graph Quadratic Functions

How to Graph Quadratic Functions

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

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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 \(y\).

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.

Graphing Quadratic Functions – 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 for Graphing Quadratic Functions

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

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

Download Graphing Quadratic Functions Worksheet

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

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