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.
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
x^2 = 7
x= +- 2.65
The graph will cross there
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.