# Tutor profile: Damian R.

## Questions

### Subject: Pre-Calculus

Find the vertex of the parabola y = x^2 + 6x - 2.

The x-coordinate of the parabola is given by the equation: -b/2a In this case b = 6 and a = 1 So x = -6/2 x = -3 Now to find the y-coordinate that corresponds to that x -value, we will plug it into the quadratic function: y= -3^2 + 6(-3) -2 y = 9 -18 -2 y = -11 Therefore the vertex is at (-3,-11) .

### Subject: Pre-Algebra

10x + 2(x-8) = 0 Solve for x

First distribute the 2 to the terms in parenthesis: 10x + 2x - 16 = 0 Combine Like Terms: 12x - 16 = 0 Move the 16 to the other side: 12x = 16 Divide by 12 to isolate the x: x = 16/12 simplify by dividing the numerator and denominator by 4: x = 4/3

### Subject: Algebra

x - 7y = -11 5x + 2y = -18 Find the coordinate pair that satisfies the system above?

Solve for x in the first equation by first adding the -7y over to the other side: x = 7y - 11 Substitute the equation above into x in the second equation: 5( 7y - 11 ) + 2y = -18 Distribute the 5: 35y - 55 + 2y = -18 Combine like terms: 37y = 37 Divide by 37 to solve for y: y = 1 Plug y = 1 into the first equation in the system: x - 7 = -11 Add the 7 over: x = -4 Therefore, the coordinate pair that satisfies this system is (-4 , 1).

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