Question

Find the vertex of the parabola. y = negative 4 x squared + 24 x minus 35 a. ( -3, 1) c. ( 3, 1) b. ( -3, -1) d. ( -1, -3)

Answer 1

Answer:

(3, 1)

Step-by-step explanation:

y = -4x² + 24x - 35

Find the vertex by using the formula:

• (h, k) → $\displaystyle \Big [ -\frac{b}{2a}, \ f \Big (-\frac{b}{2a} \Big ) \Big ]$

In this problem, we have:

• a = -4
• b = 24
• c = -35

Using 24 for b and -4 for a, we can substitute these values into the vertex formula:

• $\displaystyle -\frac{b}{2a} \rightarrow -\frac{24}{2(-4)} = \frac{-24}{-8} = 3$

The h-value for the vertex is 3.

Now let's plug 3 back into the standard form equation to solve for the k-value of the vertex.

• $-4x^2 + 24x - 35 \rightarrow -4(3)^2+24(3)-35 = -36 + 72 - 35 = 1$

The k-value for the vertex is 1.

The vertex of the parabola is (3, 1).