Question

Complete the square to identify the two values that solve the following quadratic equation: x^2−16x−13=4
.(1 point)
x=

Answer 1

what does x equal

Answer 2

Which of the following is a solution to the quadratic equation 4x2+2x=10
? Assume that the solution has been rounded to the nearest hundredth, if applicable.(1 point)
Responses

x=1.15
x equals 1.15

x=−1.85
x equals negative 1.85

x=−0.77
x equals negative 0.77

x=1.04

Answer 3

Use the image to answer the question.

A parabola is graphed on a coordinate plane. The x-axis ranges from negative 2 to 10 in increments of 1. The y-axis ranges from negative 8 to 3 in increments of 1.

Identify these key features of the parabola.

(2 points)
vertex: (
)

(smaller) x-intercept: (
)

(larger) x-intercept: (
)

y-intercept: (
)

Answer 4

To solve the quadratic equation \( x^2 - 16x - 13 = 4 \) by completing the square, we first rearrange the equation:

\[
x^2 - 16x - 13 - 4 = 0
\]

This simplifies to:

\[
x^2 - 16x - 17 = 0
\]

Next, we can isolate the quadratic and linear terms:

\[
x^2 - 16x = 17
\]

Now, to complete the square, we need to take the coefficient of \( x \) (which is \(-16\)), divide it by \(2\) and square it:

\[
\left(\frac{-16}{2}\right)^2 = 8^2 = 64
\]

We then add \(64\) to both sides of the equation:

\[
x^2 - 16x + 64 = 17 + 64
\]

This simplifies to:

\[
(x - 8)^2 = 81
\]

Now, we take the square root of both sides:

\[
x - 8 = \pm 9
\]

This gives us two equations to solve for \(x\):

1. \(x - 8 = 9\)
2. \(x - 8 = -9\)

Solving each equation:

1. \(x = 9 + 8 = 17\)
2. \(x = -9 + 8 = -1\)

Thus, the two values that solve the equation are:

\[
\boxed{17} \quad \text{and} \quad \boxed{-1}
\]