The equation f(x) = 3x² - 24x + 8 represents a parabola. What is the vertex of the parabola?

Solution:

The vertex of the parabola is given as the coordinates (h,k).

The standard form of the x-coordinate of the vertex of a parabola is

x = -b/2a

and k = f(h)

f(x) = 3x² - 24x + 8 [Given]

We get

a = 3

b = -24

c = 8

Substituting It in the formula

x = - (-24)/ 2 (3)

x = 24/6

x = 4

Substituting x = 4 in the equation

f(4) = k = 3(4)² - 24 (4) + 8

By further calculation

k = 48 - 96 + 8

= -40

Therefore, the vertex of the parabola is (4, -40).

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The equation f(x) = 3x² - 24x + 8 represents a parabola. What is the vertex of the parabola?

Summary:

The equation f(x) = 3x² - 24x + 8 represents a parabola. The vertex of the parabola is (4, -40).