There are many strategies that can be used to sketch the graph of a parabola. In most cases, the fastest approach is to use the step pattern (1, 3, 5, 7,...) method. To sketch the graph of a parabola using this method, we first write our equation in vertex form. Once this is done, we can plot our vertex and find additional points using the pattern.

Test Objectives
• Demonstrate an understanding of how to write a parabola in vertex form
• Demonstrate the ability to sketch the graph of a parabola
• Demonstrate the ability to find the equation of a parabola from its graph
• Demonstrate the ability to find the equation of a parabola from its vertex and a point
Graphing a Parabola Practice Test:

#1:

Instructions: Sketch the graph of each.

$$a)\hspace{.2em}f(x)=x^2 + 12x + 35$$

$$b)\hspace{.2em}f(x)=x^2 - 6x + 8$$

#2:

Instructions: Sketch the graph of each.

$$a)\hspace{.2em}f(x)=2x^2 - 32x + 126$$

$$b)\hspace{.2em}f(x)=-2x^2 + 16x - 29$$

#3:

Instructions: Sketch the graph of each.

$$a)\hspace{.2em}f(x)=\frac{1}{2}x^2 + 4x + 7$$

$$b)\hspace{.2em}f(x)=-\frac{1}{2}x^2 - 3x - \frac{9}{2}$$

#4:

Instructions: Find the equation of the parabola in vertex form.

$$a)\hspace{.2em}$$ Desmos Link for More Detail

$$b)\hspace{.2em}$$ Desmos Link for More Detail

#5:

Instructions: Find the equation of the parabola in vertex form.

$$a)\hspace{.2em}$$ Vertex: $$(-5, -5)$$ Point on the Parabola: $$(-4,-7)$$

$$b)\hspace{.2em}$$ Vertex: $$(-2, 1)$$ Point on the Parabola: $$(2, 7)$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}$$

$$f(x) = x^2 + 12x + 35$$

$$b)\hspace{.2em}$$

$$f(x) = x^2 - 6x + 8$$

#2:

Solutions:

$$a)\hspace{.2em}$$

$$f(x) = 2x^2 - 32x + 126$$

$$b)\hspace{.2em}$$

$$f(x) = -2x^2 + 16x - 29$$

#3:

Solutions:

$$a)\hspace{.2em}$$

$$f(x) = \frac{1}{2}x^2 + 4x + 7$$

$$b)\hspace{.2em}$$

$$f(x) = -\frac{1}{2}x^2 - 3x - \frac{9}{2}$$

#4:

Solutions:

$$a)\hspace{.2em}f(x) = (x - 3)^2$$

$$b)\hspace{.2em}f(x) = (x - 4)^2 - 2$$

#5:

Solutions:

$$a)\hspace{.2em}f(x) = -2(x + 5)^2 - 5$$

$$b)\hspace{.2em}f(x) = \frac{3}{8}(x + 2)^2 + 1$$