# SOLUTION: Find the x- and y- intercepts for the quadratic equation y = x^2 + 6x + 8

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 Question 114163: Find the x- and y- intercepts for the quadratic equation y = x^2 + 6x + 8Answer 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: . . and set x = 0 to get that: . . The first two terms on the right side equal zero so the equation reduces to: . . This means the graph crosses the y-axis at +8 on the y-axis. . 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: . . and transposing this equation (switching sides just to get it into a little more familiar format) results in: . . Notice that the left side can be factored to convert the equation to: . . [You can multiply out the left side, just to make sure we factored it correctly, if you would like to.] . 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. . So set each of the factors equal to zero. First: . . which, by subtracting 4 from both sides, becomes: . . Then, set: . . which, by subtracting 2 from both sides, becomes: . . This tells us that the x-axis intercepts cross the x-axis at -4 and -2. . The graph for the original equation is: . . Notice where the x and y axis intercepts are. They match the work that we did. . Hope this helps you to understand the problem and how to get the answers. .