(-5x^(2)+x+3)-(4x^(2)-7x+1)=ax^(2)+bx+c where a,b, and c are constants. What is the value of b ? Choose 1 answer: (A) -9 (B) -6 (C) 7 (D) 8

Subtract and Combine Like Terms: Subtract the second polynomial from the first one by combining like terms. (-5x^2 + x + 3) - (4x^2 - 7x + 1) = ax^2 + bx + c First, combine the x^2 terms: -5x^2 - 4x^2 = -9x^2 Then, combine the x terms: x - (-7x) = x + 7x = 8x Finally, combine the constant terms: 3 - 1 = 2 So, the expression becomes -9x^2 + 8x + 2 = ax^2 + bx + cIdentify Coefficients: Identify the coefficients of x^2, x, and the constant term to find a, b, and c. From the expression -9x^2 + 8x + 2, we can see that: a = -9, b = 8, and c = 2

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(-5x^(2)+x+3)-(4x^(2)-7x+1)=ax^(2)+bx+c
where
a,b, and
c are constants. What is the value of
b ?
Choose 1 answer:
(A) -9
(B) -6
(C) 7
(D) 8

$\left(-5 x^{2}+x+3\right)-\left(4 x^{2}-7 x+1\right)=a x^{2}+b x+c$ $\newline$ where $a, b$ , and $c$ are constants. What is the value of $b$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-9$ $\newline$ (B) $-6$ $\newline$ (C) $7$ $\newline$ (D) $8$

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Algebra 1

Transformations of quadratic functions

Full solution

\left(-5 x^{2}+x+3\right)-\left(4 x^{2}-7 x+1\right)=a x^{2}+b x+c

\newline

where

a, b

, and

c

are constants. What is the value of

b

\newline

Choose

1

answer:

\newline

(A)

-9

\newline

(B)

-6

\newline

(C)

7

\newline

(D)

8

Subtract and Combine Like Terms: Subtract the second polynomial from the first one by combining like terms. $\newline$ $(-5x^2 + x + 3) - (4x^2 - 7x + 1) = ax^2 + bx + c$ $\newline$ First, combine the $x^2$ terms: $-5x^2 - 4x^2 = -9x^2$ $\newline$ Then, combine the $x$ terms: $x - (-7x) = x + 7x = 8x$ $\newline$ Finally, combine the constant terms: $3 - 1 = 2$ $\newline$ So, the expression becomes $-9x^2 + 8x + 2 = ax^2 + bx + c$
Identify Coefficients: Identify the coefficients of $x^2$ , $x$ , and the constant term to find $a$ , $b$ , and $c$ . From the expression $-9x^2 + 8x + 2$ , we can see that: $a = -9$ , $b = 8$ , and $c = 2$