Understanding Parabolas and Linear Equations

This video tutorial covers solutions for a unit one review in Math 3, focusing on linear equations, parabolas, absolute value, and exponential functions. It explains how to write equations from graphs, determine slopes, and understand vertex forms. The tutorial also covers graphing techniques, including determining domain and range, and provides step-by-step solutions for various math problems.

What is the equation of a horizontal line that crosses the Y-axis at 2?

• Y = 2

• Y = -2

• Y = X + 2

• X = 2

If a line crosses the X-axis at -3, what is the X-intercept?

• 2

• -3

• 3

• 0

What is the general form of a linear equation in point-slope form?

• y = ax^2 + bx + c

• y - k = m(x - h)

• y = a|x - h| + k

• y = mx + b

How do you calculate the slope from a graph?

• Difference of x and y

• Sum of x and y

• Rise over run

• Run over rise

What is the vertex form of a parabola?

• y = mx + b

• y = a(x - h)^2 + k

• y = ax^2 + bx + c

• y = a|x - h| + k

If a parabola has a vertex at (0,0) and a stretch factor of 2, what is its equation?

• y = 2x^2

• y = x^2 + 2

• y = 2(x - 0)^2

• y = (x - 2)^2

How do you determine the stretch factor of a parabola from a graph?

• By the vertex

• By the intercepts

• By the distance from the vertex to a point

• By the slope

What is the equation of an absolute value function with a vertex at (3, -2) and a slope of 2/3?

• y = 2/3|x - 3| - 2

• y = 3/2|x - 3| + 2

• y = 2|x - 3| - 2

• y = |x - 3| + 2

What is the general form of an exponential function?

• y = a(x - h)^2 + k

• y = a^x + k

• y = a^x

• y = a|x - h| + k

How do you determine the domain of a linear equation?

• By the intercepts

• By the extent of the graph on the X-axis

• By the slope

• By the range