What is the x-coordinate of the vertex of the parabola whose equation is y = 3x² + 9x?

Solution:

Given y = 3x² + 9x

We can take 3 as common from the terms

y = 3(x² + 3x)

Take sample values of x and y and plot the graph

In order to get apex/vertex we need to equate differentiation of y to 0

⇒ y’ = 6(x) + 9 = 0

⇒ 6x = -9

⇒ x = -9/6

⇒ x = -3/2

Put x = -3/2 in y = 3x² + 9x

⇒ y = 3(-3/2)² + 9(-3/2)

⇒ y = 27/4 - 27/2

⇒ y = -27/4

Therefore, the vertex is at (-3/2, -27/4)

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What is the x-coordinate of the vertex of the parabola whose equation is y = 3x² + 9x?

Summary:

The x-coordinate of the vertex of the parabola whose equation is y = 3x² + 9x is -3/2.