Question

Write the quadratic function f(x) = x2 - 5x + 3 in vertex form. Complete the square to determine the maximum or minimum value of the function defined by the expression. −x2 − 6x + 6

Answer 1

Answer:

a). Vertex form f the function f(x) = (x - 2.5)²+3.25

b). Maximum value of the function is (-3)

Step-by-step explanation:

a). f(x) = x² - 5x + 3

we have to write this function in the vertex form.

f(x) = x² - 2(2.5)x + 3

    = [(1)²x²- 2(2.5)x + (2.5)²-(2.5)²] + 3

    = (x - 2.5)²- 6.25 + 3

    = (x - 2.5)² - 3.25

So the vertex for of the function is

f(x) = (x - 2.5)² - 3.25

b). Given quadratic function f(x) = -x² - 6x + 6 is in the standard form of f(x) = ax² + bx + c.

By comparing the coefficients of both the functions,

a = -1, b = 6 and c = 6

Here the value of a is negative, therefore, the given parabola is opening downwards.

And the maximum will occur at

$x=-\frac{b}{2a}$

When we plug in the values,

$x=-\frac{6}{2(-1)}$

x = 3

Now to get the value of maximum of the function we will get the value of f(3).

f(3) = -(3)²- 6(3) + 6

f(3) = 9 - 18 + 6

f(3) = -3

Therefore, maximum value of the quadratic function is (-3).