Write a quadratic function that represents a parabola that opens upward and has x-intercepts (-8,0) and (-1,0)
1 answer:
The x intercepts give a clue to find the equation. We know that factored quadratic equations are written in the form (x+n)(x+n)=0, where n is a positive or negative number. This means that when you solve for x, you must handle each bracket individually, like this:
x+n=0
x=-n
This gives us the x intercept of (-n, 0)
Using this example, we notice that the coordinate of x on the x intercept is the opposite of the number in the parentheses. So, the factored form of an equation going through the x intercepts (-8,0) and (-1,0) is (x+8)(x+1). Now, we just expand the brackets to give us the full equation:
x+n=0
x=-n
This gives us the x intercept of (-n, 0)
Using this example, we notice that the coordinate of x on the x intercept is the opposite of the number in the parentheses. So, the factored form of an equation going through the x intercepts (-8,0) and (-1,0) is (x+8)(x+1). Now, we just expand the brackets to give us the full equation:
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