The vertex form of a parabola is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

In the given equation y = a(x - 6)(x + 3), we can expand it to find the vertex form.

y = a(x² - 3x - 18x + 18)

Simplify to get:

y = a(x² - 21x + 18)

To complete the square, we take half of the coefficient of x, square it and add and subtract it inside the bracket:

y = a[(x² - 21x + (21/2)²) - (21/2)² + 18]

Simplify to get:

y = a[(x - 21/2)² - (21/2)² + 18]

This is now in the form y = a(x - h)² + k, so we can see that k = a[-(21/2)² + 18]

Simplify to get:

k = a[-441/4 + 72]

k = a[-441/4 + 288/4]

k = a[-153/4]

So, k = -153a/4, which is not one of the options given. There might be a mistake in the question or the options provided.

Question

The vertex form of a parabola is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

In the given equation y = a(x - 6)(x + 3), we can expand it to find the vertex form.

y = a(x² - 3x - 18x + 18)

Simplify to get:

y = a(x² - 21x + 18)

To complete the square, we take half of the coefficient of x, square it and add and subtract it inside the bracket:

y = a[(x² - 21x + (21/2)²) - (21/2)² + 18]

Simplify to get:

y = a[(x - 21/2)² - (21/2)² + 18]

This is now in the form y = a(x - h)² + k, so we can see that k = a[-(21/2)² + 18]

Simplify to get:

k = a[-441/4 + 72]

k = a[-441/4 + 288/4]

k = a[-153/4]

So, k = -153a/4, which is not one of the options given. There might be a mistake in the question or the options provided.

Knowee AI · Accepted Answer

The vertex form of a parabola is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

In the given equation y = a(x - 6)(x + 3), we can expand it to find the vertex form.

y = a(x² - 3x - 18x + 18)

Simplify to get:

y = a(x² - 21x + 18)

To complete the square, we take half of the coefficient of x, square it and add and subtract it inside the bracket:

y = a[(x² - 21x + (21/2)²) - (21/2)² + 18]

Simplify to get:

y = a[(x - 21/2)² - (21/2)² + 18]

This is now in the form y = a(x - h)² + k, so we can see that k = a[-(21/2)² + 18]

Simplify to get:

k = a[-441/4 + 72]

k = a[-441/4 + 288/4]

k = a[-153/4]

So, k = -153a/4, which is not one of the options given. There might be a mistake in the question or the options provided.

y = a(x - 6)(x + 3)In the quadratic equation above, a is a nonzero constant. The graph of the equation in the xy-plane is a parabola with vertex (h, k). Which of the following is equal to k, in terms of a ? (A) (-9a / 4) - 15(B) -6a / 5(C) (-9a / 4) - 18a(D) 18a