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Describing Quadratic Functions

Describing Quadratic Functions 1.10 - Solution

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We are given the quadratic function and we need to write it in factored form. In the equation above, and represent the solutions to the equation Hence, we begin by finding the solutions using the quadratic formula. In our case, and Let's substitute these values into the formula above.
Simplify right-hand side
The -intercepts of the function are Let's separate them using the positive and negative signs.
The parabola intercepts the -axis at and In other words, and We are ready to rewrite the given function in factored form. Next, we find the axis of symmetry by finding the midpoint between the -intercepts. From the above, we also know that the -coordinate of the vertex is and the -coordinate is equal to Let's find the -coordinate.
Simplify right-hand side
We now know that the vertex is at Finally, we can find the -intercept by setting in The graph intercepts the -axis at With all this information, we can graph the function.