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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The two inequalities can be rewritten as
The solution is composed by every point below the graph of the line , and above the horizontal line
To draw the line we can build a little table (only 2 points are required):
So, if you draw the points (0,2) and (1, -2) and connect them, you'll have your line.
To draw the line , simply pick any point with y coordinate -2, for example (0, -2), and draw a horizontal line.
Choose the above/below areas as specified above to solve the system.
