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14 select the correct answer. what are the factors of the quadratic function represented by this graph? the graph of a quadratic function with a maximum value at the point (3,4) a. (x ? 1) and (x ? 5) b. (-x ? 1) and (x 5) c. (x ? 1) and (x 5) d. (-x 1) and (x ? 5)

User Sinitsynsv
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Answer:

Explanation:

The factors of a quadratic function can be determined by analyzing the x-intercepts or roots of the function. These are the values of x where the graph of the function intersects the x-axis.

In this case, the graph of the quadratic function has a maximum value at the point (3,4). This means that the function opens downwards and has two x-intercepts.

To find the x-intercepts, we need to determine the values of x when the graph intersects the x-axis. Since the maximum value occurs at x = 3, the x-intercepts must be symmetrically located around this point.

Let's consider the options given:

a. (x ? 1) and (x ? 5)

b. (-x ? 1) and (x 5)

c. (x ? 1) and (x 5)

d. (-x 1) and (x ? 5)

We can eliminate options b and d because they have incorrect signs.

Now, let's test the remaining options:

a. (x ? 1) and (x ? 5)

If we substitute x = 1 into the first factor, we get (1 ? 1) = 0. This means that (x ? 1) is a factor of the quadratic function.

Similarly, if we substitute x = 5 into the second factor, we get (5 ? 5) = 0. This means that (x ? 5) is also a factor of the quadratic function.

Therefore, option a. (x ? 1) and (x ? 5) is the correct answer.

User Spencer Easton
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