Find the vertex and axis of symmetry of f(x) = -3x² + 12x - 6?

Solution:

Given, the function is f(x) = -3x² + 12x - 6 --- (1)

We have to identify the vertex and the axis of symmetry of the function.

The equation of the parabola in quadratic form is given by

y = ax² + bx + c --- (2)

The vertex is (h, k)

Where h = -b/2a and k = (4ac - b²)/4a.

Comparing (1) and (2)

a = -3, b = 12, c = -6

So, h = -12/2(-3)

= -12/-6

= 2

4ac = 4(-3)(-6)

4ac = 72

So, k = [72 - (12)²]/4(-3)

k = (72 - 144)/(-12)

k = -72/-12

k = 6

Thus, (h, k) = (2, 6)

The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves.

The axis of symmetry always passes through the vertex of the parabola.

x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

So, the axis of symmetry is x = 2

Therefore, the vertex is (2, 6) and the axis of symmetry is x = 2.

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Find the vertex and axis of symmetry of f(x) = -3x² + 12x - 6?

Summary:

The vertex and axis of symmetry of f(x) = -3x² + 12x - 6 are (2, 6) and x = 2.