Graphing Quadratic Functions

Graphing Quadratic Functions

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.

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

Download Graphing Quadratic Functions Worksheet

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

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