Question

Number One)

Answer 1

Answer:

Step-by-step explanation:

(1) $f(x) = (x-1)^{2} - 36$

First, let's expand the expression:

$f(x) = x^{2} -2x + 1 - 36$

$f(x) = x^{2} - 2x - 35$

Next, let's factor the quadratic:

$f(x) = (x - 7)(x + 5)$

Finally, set the equation equal to $0$ to find the solutions

$0 = (x - 7)(x + 5)$

$x = -5, 7$

(2) During the step $(x - 5)^{2} = 36$, when you take the square root of both sides, you have two equations, rather than one:

$x - 5 = 6$ and $x - 5 = -6$, so the solutions should be $x = -1, 11$

(3)

$\frac{1}{4}(x + 5)^{2} - 1 = 3$

Add $1$ to both sides

$\frac{1}{4}(x + 5)^{2} = 4$

Multiply both sides by $4$

$(x + 5)^{2} = 16$

Take the square root of both sides

$x + 5 =$±$4$

Subtract $5$ from both sides

$x = -9, -1$