If f(x) = x2 − 1, and f(2a) = 35, then what could be the value of a ?

1 answer:

6 0

F(2a)=35
35=(2a)^2-1
35=4a^2-1
minus 35 from both sidse
0=4a^2-36
facor out 4
0=4(a^2-9)
factor differece of 2 perfect squares
0=4(a-3)(a+3)
set to zero
a-3=0
a=3

a+3=0
a=-3

a=-3 or 3

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Answer:

$(x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}$

$(x,y)=\left(\; \boxed{5,16} \; \right)\quad \textsf{(larger $x$-value)}$

Step-by-step explanation:

Given system of equations:

$\begin{cases}y=x^2-9\\y=4x-4\end{cases}$

To solve by the method of substitution, substitute the first equation into the second equation and rearrange so that the equation equals zero:

$\begin{aligned}x^2-9&=4x-4\\x^2-4x-9&=-4\\x^2-4x-5&=0\end{aligned}$