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madreJ [45]
3 years ago
8

Explain how you could write a quadratic function in factored form that would have a vertex with an x-coordinate of 3 and two dis

tinct roots.

Mathematics
2 answers:
Inga [223]3 years ago
8 0

Answer:

answer below

Step-by-step explanation:

The vertex lies on the axis of symmetry, so the axis of symmetry is x = 3. Find any two x-intercepts that are equal distance from the axis of symmetry. Use those  x-intercepts to write factors of the function by subtracting their values from x. For example, 2 and 4 are each 1 unit from x = 3, so f(x) =  (x – 2)(x – 4) is a possible function.

skad [1K]3 years ago
4 0
<span>The definition of quadratic function is given by:

</span>(1) \ f(x)=ax^{2}+bx+c \\ \\ where \ a, b, c \ are \ real \ values<span>

So the problem asks for two conditions:

<em>1. Write the quadratic function in factored form. </em>
<em>2. The vertex has an x-coordinate of 3.</em>

Then the equation (1) must be written as follows:

</span>f(x)=(x-m)(x-n) \\ \\ where \ m \ and \ n \ are \ the \ roots<span>

To satisfy the two conditions:

\frac{m+n}{2}=3

So we are free to choose the value of one root, say:

m=1

Thus:

n=6-1=5

Finally, the answer is:

f(x)=(x-1)(x-5)

The graph of this function is shown in the figure below.</span>

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