How do you graph the function h(x)=x^2-7

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embizze's profile pic

embizze | High School Teacher | (Level 2) Educator Emeritus

Posted on

Graph the function h(x)=x^2-7:

This function is a quadratic function -- the variable appears to the second degree.

The graph of a quadratic function is a parabola.

There are a number of tips and techniques you can use to graph this:

(1) If you know what the graph of y=x^2 looks like, then h(x) is the same graph translated down 7 units.

(2) Since the expression x^2-7 is in standard form, you can locate the axis of symmetry and the vertex.

If the expression is in the form ax^2+bx+c, the axis of symmetry is the vertical line x=(-b)/(2a). In this case a=1 and b=0, so the axis is x=0 or the y-axis.

The vertex is on the axis of symmetry -- if x=0 then h(0)=-7 so the vertex is at (0,-7)

(3) You can find a few points -- this is easier if you have already located the vertex since you can use symmetry.

x     | -3   -2   -1    0    1    2   3
h(x) |  2   -3   -6   -7   -6   -3   2

Thus the points (-3,2),(-2,-3), etc... all lie on the parabola. 

The graph:


atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on


Looking at this problem alone we can already tell the shape of the graph

Anytime the highest degree in a problem is a 2, it means we have a parabola

therefore the graph will be a curve facing upward as the leading coefficient is a positive (1)

The -7 tells us the y intercept, this will be where the graph crosses the y axis.

Now all we need to find are the x intercepts.

all you have to do is set the equation equal to zero and solve:

x^2 - 7 = 0

subtract 7

x^2 = 7


x= +- 2.65

The graph will cross there


messian's profile pic

messian | eNotes Newbie

Posted on

First you have to make the graph of h(x)=x^2. Then bring the whole graph down by 7 units. Thus you will get your required graph.

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