The equation f(x) = 5x² - 30x + 6 represents a parabola. What is the vertex of the parabola?
(-5, 281), (5, -19), (-3, 141), (3, -39)

Solution:

Given:  f(x) = 5x² - 30x + 6 is the equation of the parabola

the vertex of a parabola is represented as (h, k)

Where h = -b/2a and k = f(h)

Comparing with general equation ax² + bx+ c, we get

a = 5, b = -30, c = 6

We know that

x = -b/2a

Substituting the values

x = -(-30)/ 2(5)

x = 30/10

x = 3

Substitute the value of x in the given equation

f(3) = 5(3)² - 30(3) + 6

f(3) = 45 - 90 + 6

f(3) = 51 - 90

f(3) = -39

Therefore, the vertex of the parabola is (3, -39).

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The equation f(x) = 5x² - 30x + 6 represents a parabola. What is the vertex of the parabola?

Summary:

The equation f(x) = 5x² - 30x + 6 represents a parabola. The vertex of the parabola is (3, -39).