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bulgar [2K]
4 years ago
13

Write the quadratic function f(x) = x2 - 5x + 3 in vertex form.

Mathematics
1 answer:
Nuetrik [128]4 years ago
4 0

Answer:

C. f(x) = (x-2.5)^{2}-3.25

Step-by-step explanation:

The vertex form for a quadratic function is:

f(x) = a(x-h)^2+k

  • Then, you expand the binomial and get:

f(x) = a(x^2-2hx +h^2) + k

  • Now you distribute and get the first form:

f(x) = ax^2-2ahx +ah^2 + k

  • You know that the general form for a quadratic function is:

f(x) = ax^2+bx+c, Second\ form

  • You compare the two forms that you have and finding h and k:

ax^2+2ahx +ah^2 + k = ax^2+bx+c

  • Finding h from the coefficient of X:

-2ah = b

h = -\frac{b}{2a}

from the quadratic function given you know that a = 1 , b = -5 and c = 3, thus:

h = -\frac{(-5)}{2(1)}=2.5

  • Finding k from the third coefficient:

ah^2+k = c

Isolate\ k =>\ k = c-ah^2

You know c,a and h, so replace the values:

k = 3-(1)(2.5)^2 \\ k = 3-6.25\\ k = -3.25\\

• Finally replace the values for a, h and k in the vertex form:

f(x) = a(x-h)^2+k\\ f(x) = (1)(x-2.5)^2+(-3.25)\\ f(x) = (x-2.5)^2-3.25

So answer is C. f(x) = (x-2.5)^2-3.25

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