Solved on Dec 15, 2023

Copy and complete the table for $y=x^{2}+4x-1$ . Find the values of $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ .

STEP 1

Assumptions
1. The function given is $y = x^{2} + 4x - 1$ .
2. We need to find the values of $y$ for $x = -3$ , $x = 0$ , and $x = 1$ to replace $\mathrm{A}$ , $\mathrm{B}$ , and $\mathrm{C}$ respectively.

STEP 2

First, we will calculate the value of $y$ when $x = -3$ to find $\mathrm{A}$ .
$y = x^{2} + 4x - 1$

STEP 3

Substitute $x = -3$ into the equation.
$y = (-3)^{2} + 4(-3) - 1$

STEP 4

Calculate the square of $-3$ .
$(-3)^{2} = 9$

STEP 5

Multiply $4$ by $-3$ .
$4(-3) = -12$

STEP 6

Add the results from STEP_4 and STEP_5 and subtract $1$ .
$y = 9 - 12 - 1$

STEP 7

Calculate the value of $y$ for $x = -3$ .
$y = 9 - 12 - 1 = -4$
So, $\mathrm{A} = -4$ .

STEP 8

Next, we will calculate the value of $y$ when $x = 0$ to find $\mathrm{B}$ .
$y = x^{2} + 4x - 1$

STEP 9

Substitute $x = 0$ into the equation.
$y = (0)^{2} + 4(0) - 1$

STEP 10

Calculate the square of $0$ and multiply $4$ by $0$ .
$(0)^{2} = 0$ $4(0) = 0$

STEP 11

Add the results from STEP_10 and subtract $1$ .
$y = 0 + 0 - 1$

STEP 12

Calculate the value of $y$ for $x = 0$ .
$y = 0 + 0 - 1 = -1$
So, $\mathrm{B} = -1$ .

STEP 13

Finally, we will calculate the value of $y$ when $x = 1$ to find $\mathrm{C}$ .
$y = x^{2} + 4x - 1$

STEP 14

Substitute $x = 1$ into the equation.
$y = (1)^{2} + 4(1) - 1$

STEP 15

Calculate the square of $1$ and multiply $4$ by $1$ .
$(1)^{2} = 1$ $4(1) = 4$

STEP 16

Add the results from STEP_15 and subtract $1$ .
$y = 1 + 4 - 1$

STEP 17

Calculate the value of $y$ for $x = 1$ .
$y = 1 + 4 - 1 = 4$
So, $\mathrm{C} = 4$ .
The completed table of values is:
\begin{tabular}{c||c|c|c|c|c} $x$ & -3 & -2 & -1 & 0 & 1 \\ \hline $y$ & -4 & -5 & -4 & -1 & 4 \end{tabular}
The numbers that replace $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are $\mathrm{A} = -4$ , $\mathrm{B} = -1$ , and $\mathrm{C} = 4$ .

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Copy and complete the table for $y=x^{2}+4x-1$ . Find the values of $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ .

STEP 1

Assumptions
1. The function given is $y = x^{2} + 4x - 1$ .
2. We need to find the values of $y$ for $x = -3$ , $x = 0$ , and $x = 1$ to replace $\mathrm{A}$ , $\mathrm{B}$ , and $\mathrm{C}$ respectively.

STEP 2

First, we will calculate the value of $y$ when $x = -3$ to find $\mathrm{A}$ .
$y = x^{2} + 4x - 1$

STEP 3

Substitute $x = -3$ into the equation.
$y = (-3)^{2} + 4(-3) - 1$

STEP 4

Calculate the square of $-3$ .
$(-3)^{2} = 9$

STEP 5

Multiply $4$ by $-3$ .
$4(-3) = -12$

STEP 6

Add the results from STEP_4 and STEP_5 and subtract $1$ .
$y = 9 - 12 - 1$

STEP 7

Calculate the value of $y$ for $x = -3$ .
$y = 9 - 12 - 1 = -4$
So, $\mathrm{A} = -4$ .

STEP 8

Next, we will calculate the value of $y$ when $x = 0$ to find $\mathrm{B}$ .
$y = x^{2} + 4x - 1$

STEP 9

Substitute $x = 0$ into the equation.
$y = (0)^{2} + 4(0) - 1$

STEP 10

Calculate the square of $0$ and multiply $4$ by $0$ .
$(0)^{2} = 0$ $4(0) = 0$

STEP 11

Add the results from STEP_10 and subtract $1$ .
$y = 0 + 0 - 1$

STEP 12

Calculate the value of $y$ for $x = 0$ .
$y = 0 + 0 - 1 = -1$
So, $\mathrm{B} = -1$ .

STEP 13

Finally, we will calculate the value of $y$ when $x = 1$ to find $\mathrm{C}$ .
$y = x^{2} + 4x - 1$

STEP 14

Substitute $x = 1$ into the equation.
$y = (1)^{2} + 4(1) - 1$

STEP 15

Calculate the square of $1$ and multiply $4$ by $1$ .
$(1)^{2} = 1$ $4(1) = 4$

STEP 16

Add the results from STEP_15 and subtract $1$ .
$y = 1 + 4 - 1$

STEP 17

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Copy and complete the table for y=x2+4x−1y=x^{2}+4x-1y=x2+4x−1. Find the values of A,B\mathrm{A}, \mathrm{B}A,B and C\mathrm{C}C.

STEP 1

Assumptions1. The function given is y=x2+4x−1y = x^{2} + 4x - 1y=x2+4x−1.2. We need to find the values of yyy for x=−3x = -3x=−3, x=0x = 0x=0, and x=1x = 1x=1 to replace A\mathrm{A}A, B\mathrm{B}B, and C\mathrm{C}C respectively.

STEP 2

First, we will calculate the value of yyy when x=−3x = -3x=−3 to find A\mathrm{A}A.y=x2+4x−1y = x^{2} + 4x - 1y=x2+4x−1

STEP 3

Substitute x=−3x = -3x=−3 into the equation.y=(−3)2+4(−3)−1y = (-3)^{2} + 4(-3) - 1y=(−3)2+4(−3)−1

STEP 4

Calculate the square of −3-3−3.(−3)2=9(-3)^{2} = 9(−3)2=9

STEP 5

Multiply 444 by −3-3−3.4(−3)=−124(-3) = -124(−3)=−12

STEP 6

Add the results from STEP_4 and STEP_5 and subtract 111.y=9−12−1y = 9 - 12 - 1y=9−12−1

STEP 7

Calculate the value of yyy for x=−3x = -3x=−3.y=9−12−1=−4y = 9 - 12 - 1 = -4y=9−12−1=−4So, A=−4\mathrm{A} = -4A=−4.

STEP 8

Next, we will calculate the value of yyy when x=0x = 0x=0 to find B\mathrm{B}B.y=x2+4x−1y = x^{2} + 4x - 1y=x2+4x−1

STEP 9

Substitute x=0x = 0x=0 into the equation.y=(0)2+4(0)−1y = (0)^{2} + 4(0) - 1y=(0)2+4(0)−1

STEP 10

Calculate the square of 000 and multiply 444 by 000.(0)2=0 (0)^{2} = 0 (0)2=0 4(0)=0 4(0) = 0 4(0)=0

STEP 11

Add the results from STEP_10 and subtract 111.y=0+0−1y = 0 + 0 - 1y=0+0−1

STEP 12

Calculate the value of yyy for x=0x = 0x=0.y=0+0−1=−1y = 0 + 0 - 1 = -1y=0+0−1=−1So, B=−1\mathrm{B} = -1B=−1.

STEP 13

Finally, we will calculate the value of yyy when x=1x = 1x=1 to find C\mathrm{C}C.y=x2+4x−1y = x^{2} + 4x - 1y=x2+4x−1

STEP 14

Substitute x=1x = 1x=1 into the equation.y=(1)2+4(1)−1y = (1)^{2} + 4(1) - 1y=(1)2+4(1)−1

STEP 15

Calculate the square of 111 and multiply 444 by 111.(1)2=1 (1)^{2} = 1 (1)2=1 4(1)=4 4(1) = 4 4(1)=4

STEP 16

Add the results from STEP_15 and subtract 111.y=1+4−1y = 1 + 4 - 1y=1+4−1

STEP 17

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Copy and complete the table for $y=x^{2}+4x-1$ . Find the values of $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ .

Assumptions
1. The function given is $y = x^{2} + 4x - 1$ .
2. We need to find the values of $y$ for $x = -3$ , $x = 0$ , and $x = 1$ to replace $\mathrm{A}$ , $\mathrm{B}$ , and $\mathrm{C}$ respectively.

First, we will calculate the value of $y$ when $x = -3$ to find $\mathrm{A}$ .
$y = x^{2} + 4x - 1$

Substitute $x = -3$ into the equation.
$y = (-3)^{2} + 4(-3) - 1$

Calculate the square of $-3$ .
$(-3)^{2} = 9$

Multiply $4$ by $-3$ .
$4(-3) = -12$

Add the results from STEP_4 and STEP_5 and subtract $1$ .
$y = 9 - 12 - 1$

Calculate the value of $y$ for $x = -3$ .
$y = 9 - 12 - 1 = -4$
So, $\mathrm{A} = -4$ .

Next, we will calculate the value of $y$ when $x = 0$ to find $\mathrm{B}$ .
$y = x^{2} + 4x - 1$

Substitute $x = 0$ into the equation.
$y = (0)^{2} + 4(0) - 1$

Calculate the square of $0$ and multiply $4$ by $0$ .
$(0)^{2} = 0$ $4(0) = 0$

Add the results from STEP_10 and subtract $1$ .
$y = 0 + 0 - 1$

Calculate the value of $y$ for $x = 0$ .
$y = 0 + 0 - 1 = -1$
So, $\mathrm{B} = -1$ .

Finally, we will calculate the value of $y$ when $x = 1$ to find $\mathrm{C}$ .
$y = x^{2} + 4x - 1$

Substitute $x = 1$ into the equation.
$y = (1)^{2} + 4(1) - 1$

Calculate the square of $1$ and multiply $4$ by $1$ .
$(1)^{2} = 1$ $4(1) = 4$

Add the results from STEP_15 and subtract $1$ .
$y = 1 + 4 - 1$