Question Determine if $(-1,29)$ is a solution to the quadratic equation $y=-2x^2-5x+22$ . Show your work.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $y = -2x^2 - 5x + 22$ .
2. We need to check if the point $(-1, 29)$ is a solution to the given equation.

STEP 2

To determine if $(-1, 29)$ is a solution to the equation, we need to substitute $x = -1$ into the equation and check if the resulting value of $y$ is equal to $29$ .

STEP 3

Substitute $x = -1$ into the equation.
$y = -2(-1)^2 - 5(-1) + 22$

STEP 4

Calculate the square of $-1$ .
$(-1)^2 = 1$

STEP 5

Replace $(-1)^2$ with $1$ in the equation.
$y = -2(1) - 5(-1) + 22$

STEP 6

Multiply $-2$ by $1$ .
$-2 \times 1 = -2$

STEP 7

Replace $-2(1)$ with $-2$ in the equation.
$y = -2 - 5(-1) + 22$

STEP 8

Multiply $-5$ by $-1$ .
$-5 \times -1 = 5$

STEP 9

Replace $-5(-1)$ with $5$ in the equation.
$y = -2 + 5 + 22$

STEP 10

Add the numbers together to find the value of $y$ .
$y = -2 + 5 + 22 = 3 + 22$

STEP 11

Complete the addition.
$y = 3 + 22 = 25$

STEP 12

Compare the calculated value of $y$ with the $y$ -coordinate of the given point $(-1, 29)$ .

STEP 13

Since the calculated value of $y$ is $25$ and the $y$ -coordinate of the point is $29$ , they do not match.

STEP 14

Conclude that $(-1, 29)$ is not a solution to the equation $y = -2x^2 - 5x + 22$ because when $x = -1$ , the value of $y$ should be $25$ , not $29$ .
The point $(-1, 29)$ is not a solution to the equation $y = -2x^2 - 5x + 22$ .

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