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
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.
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.