Question 116122This question is from textbook Introductury Algebra
: Please can you help me with this equation, I've been working it out but I'm not able to get the right answer. Graph and solve the equation.
y= x^2 - 4
This question is from textbook Introductury Algebra
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Sometimes it's easier to just do a little analysis and not get lost in math. Let's try that
approach.
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First, the right side of the equation is a quadratic form (the highest power of x is the 2nd
power). From that you know that the graph will be a parabola. And since the sign on the
x-squared term is positive, you can tell that as you move from the left to the right along
the x-axis the graph will drop more and more until it reaches some low point, and then it will
start to rise more and more as you move further to the right. You also know that if you draw
a vertical line through that low point on the graph the graph to the left of that line will
look like the mirror image of the graph to the right of that line.
.
[For your information in other problems of this type, if the sign on the x-squared term
is negative, you can tell that the graph will rise to a peak and then fall back down
the further you go to the right along the x-axis.]
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Now you can just calculate some points to help you understand what the graph looks like.
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One nice and easy point on the graph can be found by setting x equal to zero and finding what
the corresponding value of y is. When you set x equal to zero in the given equation for
y, you get:
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y = (0)^2 - 4 = -4
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Now you know that the point (0, -4) is on the graph. Plot it.
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Next let's try letting x = +1 and calculate y. Substituting x into the given equation
results in:
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y = (1)^2 - 4 = 1 - 4 = -3
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This time you know that the point (1, -3) is on the graph
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Next let's set x equal to -1 and calculate the corresponding value of y.
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y = (-1)^2 - 4 = 1 - 4 = -3
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Now you know that (-1, -3) is on the graph.
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Now let's set x = 2 to find that:
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y = (2)^2 - 4 = 4 - 4 = 0
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This time you know that (2, 0) is on the graph. Then if you set x = -2 you get the corresponding
value of y to be:
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y = (-2)^2 - 4 = +4 - 4 = 0
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The point (-2, 0) is on the graph.
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If you have plotted these five points on the graph you should have a pretty good idea of what
the parabola looks like. You can use more values for x to find corresponding values of
y and get more points on the graph. With more points you should find that it looks like:
.
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If you are to "solve" this equation that means that you are looking for the value of x
where the graph crosses the x-axis. If you've done your graphing pretty accurately
you should see that the graph crosses the x-axis at two places ... where x = -2 and x = +2.
This means that for those two values of x the corresponding value of y is zero.
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Hope this helps you with a little different slant on this problem.
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