QF - Graphing Quadratics in Standard Form (Lesson)

Graphing Quadratics in Standard Form

Last module, you studied quadratic equations in standard form. So, let's think about how to graph quadratic functions in standard form.

f of x equals a times x squared plus b times x plus c.

The graph of a quadratic function is called a parabola, and it looks like this (the point where the parabola crosses the x-axis these represent the real solutions.)

Standard quadratic function graph.

So, now let's try and graph a quadratic function by making a table.

f(x) = x²
x	f(x)
-2	4
-1	1
0	0
1	1
2	4

Plot these points and sketch the curve.

A graph where you plot the points and sketch the curve.

Parabolic graphs opening up and down with a vertex. x sub v equals negative b divided by 2a, y sub equals plug in x sub v. The vertex is the highest or lowest point of the parabola, and it is the first point you should find when graphing a quadratic function. In the quadratic above, the vertex is (0, 0). But if a quadratic function is moved around, then you must use an equation to find the vertex.

Let's try finding the vertex of a quadratic function.

f(x) = 2x² - 8x +3

x_v = (-b/2a) = [-(-8)/2(2)] = 8/4 = 2

y_v = 2(2)² - 8(2) + 3 = 2(4) = -16 + 3 = 8 - 13 = -5

Watch this video to try a few problems.

Find the Vertex Practice

Find the vertex for each of the following quadratic functions.

f(x) = -x² + 2x + 3
f(x) = 3x² + 12x
f(x) = x² - 6x + 4
f(x) = 2x² - 7

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

After finding the vertex, it is important to find other key features and points.

Key Features of Quadratic Functions
Feature	Definition	Picture	How to Find it
Vertex	The highest or lowest point on the parabola.		x_v = (-b/2a) y_v = plug in x_v
Axis of Symmetry	The vertical line that passes through the vertex and splits the parabola in half		x = x_v
y - intercept	The point where the parabola crosses the y-axis		Let x = 0 and find y.
x - intercept	The point(s) where the parabola crosses the x-axis		Let y = 0 and solve for x.
Leading Coefficient	The a - value. If a<0, the parabola opens down. If a>0 the parabola opens up.		Identify a.

Watch this video to see a few examples:

Graphing Quadratic Functions in Standard Form Practice

Try these problems. Find the vertex, axis of symmetry, y - intercept, x - intercepts, and graph it.

f(x) = x²+4x + 3
f(x) = -2x² -4x + 4
f(x) = 3x² - 9

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

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