Ximena's Midterm Review

Systems of Equations

100

y= 5x+4

10x -5y= 25

x=-3

y = -11

(-3,-11)

200

Solve the next system of equations by using the elimination method:

2x + 3y= 20

4x + 7y= 48

x=-2

y=8

(-2,8)

300

3x - y = 4

2x + y = 8

x=2

y=-4

(2, -4)

400

Determine if (-2,4) is the solution to the next system of equations

4x +y =-4

-x +3y= 8

No, (-2,4) is not a solution

500

-3x +5y =15

-10y + 6x =-20

No Solution

Linear Equations

100

What is the slope-intercept form of a line?

y=mx+b

200

What is the point slope form of a line? 

(y-y₁) = m (x-x₁)

300

Equation of a line with a slope of 3/5 that goes through (5,1)

y= 3/5x - 2 

400

Write the equation of a line parallel to y= 3x-4 through (1,5)

y= 3x +2

500

Write the equation of a line perpendicular to 3y= x-6 through (2, -5)

y =-3x +1

Parent Function and Quadratics

100

What happens when in the standard form of a quadratic equation a is negative?

the parabola opens down

200

What is the equation of the vertex form of a quadratic equation?

f(x)=a (x-h)² +k

300

How do you graph a quadratic equation when a is a fraction?

Set whatever is in the parenthesis equal to the denominator of the fraction, solve it, and plug it in for x to find a point

400

Which variables are commonly used for range and domain?

y is used for range and x for domain

500

List the six shifts a parent function can do.

upward, downward, to the left, to the right, upside-down and swapping the left and right sides.

Factoring

100

a²+3a-54

(a+9)(a-6)

200

5x³ -10x² +3x -6

(5x²+3) (x-2)

300

85x⁹ + 136x⁵ + 51x

17x (5x⁸ + 8x⁴ + 3)

400

4c²+36c+80

4(c+5) (c+4)

500

6a²+13a-28

(2a+7) (3a-4)