Question

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

Answer 1

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. $f(x) = (x-2.5)^2-3.25$