What is the equation of the axis of symmetry of the graph of y + 3x - 6 = -3(x - 2)² + 4?

Solution:

The axis of symmetry is the line that divides a parabola into identical parts.

The vertex is the point (h, k) where the axis of symmetry intersects the parabola.

We will use the vertex formula of the parabola h = -b/ 2a to determine the axis of symmetry.

Step 1: Solve the equation for the value of y to get the standard form of parabola.

 ⇒ y + 3x - 6 = - 3(x - 2)² + 4

⇒ y + 3x - 6 = - 3x² + 12x - 12 + 4

⇒ y = - 3x + 6 - 3x² + 12x - 8

⇒ y = - 3x² + 9x - 2

Step 2: Using the formula h = -b/2a where b is the coefficient of x and a is the coefficient of x².

⇒ h = -b/2a

⇒ h = -9/2(-3)

Step 3: Solve for the value of h.

⇒ h = 3/2

Thus, the equation of the graph is h = 3/2 which also gives the axis of symmetry.

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What is the equation of the axis of symmetry of the graph of y + 3x - 6 = - 3(x - 2)² + 4?

Summary:

The value of h is 3/2 which is the line of symmetry of the graph of the equation y + 3x - 6 = - 3(x - 2)² + 4.