Algebra 1 help on the questions i missed on my test

Solve the quadratic equation.
12x2 - 75 = 0


Which equation represents a function?
A)
x = 4y + 7
B)
y2 = -5x - 8
C)
y = ±2x + 3
D)
y = ± square root of 3x + 8

12x² - 75 = 0 --- divide both sides by 3
4x² - 25 = 0 ----- I'm not sure if you're familiar with how to factor a difference of squares, but if you ever see a quadratic in the form of a²x² - b², then it can be quickly factored into (ax + b)(ax - b).
(2x + 5)(2x - 5) = 0
x = ± 5/2

A function is a relationship between two variables that is consistent, meaning an input will ALWAYS give a single, definite output (undefined is a valid output). The graph of

± sqrt(x)

for any x, whether it is (3x + 8) or x/7, will be a sideways parabola, so some x values have multiple outputs. You can also notice that since it takes the positive and negative value, one x can have two outputs.

y = ±2x + 3

Same explanation. X has multiple outputs.

y² = -5x - 8

This is another way of writing

y = ± sqrt(-5x - 8)

And as such, it is not a function.

All that is left is A), a perfectly normal line that is indeed a function.