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Question 114163: Find the x- and y- intercepts for the quadratic equation y = x^2 + 6x + 8
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! To get the point on the y axis where the graph crosses, set the value of x at zero and solve
the equation for the corresponding value of y. [Note that for any point on the y-axis the
value of x for that point is zero.] So to find the value of the y-intercept, you go to the
equation:
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and set x = 0 to get that:
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The first two terms on the right side equal zero so the equation reduces to:
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This means the graph crosses the y-axis at +8 on the y-axis.
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Similarly you can find the values where the graph crosses the x-axis by setting y equal to zero
because any coordinate point on the x-axis has zero for its y value. Setting y equal to zero
in the equation leads to:
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and transposing this equation (switching sides just to get it into a little more familiar
format) results in:
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Notice that the left side can be factored to convert the equation to:
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[You can multiply out the left side, just to make sure we factored it correctly, if you would
like to.]
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This factored form will be correct if either of the factors is equal to zero, because if
either factor is zero, the left side will involve a multiplication by zero ... and this
makes the entire left side equal to zero and therefore equal to the right side.
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So set each of the factors equal to zero. First:
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which, by subtracting 4 from both sides, becomes:
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Then, set:
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which, by subtracting 2 from both sides, becomes:
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This tells us that the x-axis intercepts cross the x-axis at -4 and -2.
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The graph for the original equation is:
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Notice where the x and y axis intercepts are. They match the work that we did.
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Hope this helps you to understand the problem and how to get the answers.
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