Find the vertex of the parabola whose equation is y = x² + 8x + 12.

Solution:

The standard form of a parabola is ax² + bx + c

The x-coordinate of the vertex is the equation of axis of symmetry

x = -b/2a

The given equation is y = x² + 8x + 12

a = 1, b = 8, c = 12

x = -8/2 --- (1)

x = -8/2

x = -4

Let us substitute the value of x in the given equation

f(x) = x² + 8x + 12

f(-4) = (-4)² + 8 (-4) + 12

f(-4) = 16 - 32 + 12

f(-4) = -4

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

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Find the vertex of the parabola whose equation is y = x² + 8x + 12.

Summary:

The vertex of the parabola whose equation is y = x² + 8x + 12 is (-4, -4).