Quadratic and Linear Function Concepts

The video tutorial covers various algebraic concepts, including solving inequalities, graphing functions, understanding slope and y-intercept, factoring, exponential functions, completing the square, solving literal equations, using the quadratic formula, linear regression, systems of equations, graphing inequalities, and applying quadratic equations to real-world scenarios. The tutorial provides step-by-step solutions and explanations, using a calculator for graphing and calculations.

What is the first step in solving the inequality y - 3 ≤ 2y + 1?

• Divide both sides by 4

• Multiply both sides by -1

• Subtract 2y from both sides

• Add 3 to both sides

When graphing the function f(x) = 0.5x + 3 over the interval [-8, 0], what is the y-coordinate when x = -8?

• 1

• 3

• 0

• 5

In the context of a linear function, what does the slope represent?

• The minimum value

• The rate of change

• The initial value

• The maximum value

What is the factored form of x^4 - 16 using the difference of squares?

• (x^2 + 16)(x^2 - 16)

• (x^2 + 4)(x^2 - 4)

• (x + 4)(x - 4)

• (x^2 + 2)(x^2 - 2)

What is the vertex form of a quadratic equation?

• a(x - h)^2 + k

• ax^2 + bx + c

• ax^2 - bx + c

• a(x + h)^2 - k

Using the quadratic formula, what are the roots of the equation w^2 + 3w - 11 = 0?

• 2.14 and -5.14

• 3.14 and -4.14

• 0.14 and -7.14

• 1.14 and -6.14

What is the correlation coefficient if the r value is 0.97?

• Weak positive correlation

• Strong positive correlation

• Weak negative correlation

• Strong negative correlation

If Hannah bought 6 pens, how many pencils did she buy if she bought 4 more pencils than pens?

• 8

• 6

• 10

• 12

What is the solution set for the system of inequalities y ≤ -3/4x + 5 and y < 3/2x - 2?

• The region below both lines

• The region outside the lines

• The region between the lines

• The region above both lines

What is the maximum height reached by the ball if the vertex of the quadratic is (3, 256)?

• 256 feet

• 150 feet

• 300 feet

• 112 feet