Write the equation in vertex form:

y= -3x^2+12x+15

You want to complete the square .....

y= -3x^2+12x+15
= -3(x^2 - 4x + c - c) + 15
= -3(x^2 - 4x + 4 - 4) + 15
= -3( (x-2)^2 - 4) + 15
= -3(x-2)^2 + 12 + 15
= -3(x-2)^2 + 27

You should always check your answer by expanding
the result.

Y = -3x^2 + 12x + 15.

Vertex form: Y = a(x-h)^2 + k.
a = -3.
h = -B/2A = -12/-6 = 2.
k = -3*2^2 + 12*2 + 15 = 27.

To write the equation in vertex form, we need to complete the square. Here's how you can do it step-by-step:

Step 1: Start with the equation: y = -3x^2 + 12x + 15.

Step 2: Factor out the common factor (-3) from the first two terms: y = -3(x^2 - 4x) + 15.

Step 3: To complete the square, take half of the coefficient of the x-term (-4), square it (-4/2 = -2, -2^2 = 4), and add it to both sides of the equation inside the parentheses:

y = -3(x^2 - 4x + 4 - 4) + 15.

Step 4: Rearrange the terms inside the parentheses as a perfect square trinomial:

y = -3((x - 2)^2 - 4) + 15.

Step 5: Distribute the -3 to both terms inside the parentheses:

y = -3(x - 2)^2 + 12 + 15.

Step 6: Combine like terms:

y = -3(x - 2)^2 + 27.

So, the equation in vertex form is y = -3(x - 2)^2 + 27.

To write the equation in vertex form, we need to complete the square. The general form of a quadratic equation in vertex form is:

y = a(x - h)^2 + k

Where (h, k) represents the coordinates of the vertex.

Let's complete the square:

y = -3x^2 + 12x + 15

First, we'll factor out the common factor -3 from the x terms:

y = -3(x^2 - 4x) + 15

Next, we need to take half of the coefficient of x (-4), square it, and add it inside the parentheses to complete the square. Half of -4 is -2, and (-2)^2 is 4:

y = -3(x^2 - 4x + 4 - 4) + 15

The equation inside the parentheses is a perfect square trinomial, so we can rewrite it as (x - 2)^2:

y = -3((x - 2)^2 - 4) + 15

Simplifying further:

y = -3(x - 2)^2 + 12 + 15

y = -3(x - 2)^2 + 27

Therefore, the equation in vertex form is y = -3(x - 2)^2 + 27. The vertex of the parabola is at (2, 27).