Solving Quadratics Methods

What is the first step in factoring a quadratic equation?

• Divide by the coefficient of x^2

• Find the discriminant

• Check for a common factor

• Square the coefficient of x

When completing the square, what constant is added and subtracted to the equation?

• The square of the coefficient of the linear term

• Half the coefficient of the linear term

• Twice the coefficient of the linear term

• The constant term of the equation

Tags

CCSS.HSA-REI.B.4B

What is the quadratic formula used for?

• Graphing exponential functions

• Calculating derivatives

• Solving linear equations

• Finding the roots of a quadratic equation

Tags

CCSS.HSA-REI.B.4B

How can you determine the solutions of a quadratic equation graphically?

• Count the number of vertices on the graph

• Use a pie chart to represent the solutions

• Solve for y instead of x

• Plot the quadratic equation as a parabola on a graph and find the x-intercepts.

Factor the quadratic equation: x^2 + 5x + 6

• (x + 1)(x + 6)

• (x + 4)(x + 2)

• (x + 2)(x + 3)

• (x + 3)(x + 4)

Complete the square for the quadratic equation: x^2 + 4x - 5

• (x + 4)^2 - 5

• (x + 2)^2 - 9

• (x - 2)^2 - 9

• (x + 3)^2 - 10

Tags

CCSS.HSA-REI.B.4B

Solve the quadratic equation using the quadratic formula: 2x^2 + 5x - 3 = 0

• x = 3, -1

• x = 0.5, -3

• x = -4, 2

• x = 1, -2

Tags

CCSS.HSA-REI.B.4B

Graphically represent the quadratic equation: y = x^2 - 4x + 4

• The quadratic equation y = x^2 - 4x + 4 has no real solutions.

• The graph of the quadratic equation y = x^2 - 4x + 4 is a straight line.

• The vertex of the parabola is at (0, 2).

• The graph of the quadratic equation y = x^2 - 4x + 4 is a parabola opening upwards with the vertex at (2, 0).

What method would you use to solve the quadratic equation: x^2 - 9 = 0?

• x = 3, x = -3

• x = 5, x = -5

• x = 2, x = -2

• x = 4, x = -4

Tags

CCSS.HSA-REI.B.4B

Explain the steps involved in factoring a quadratic equation.

• Dividing each term by the coefficient of x^2

• The steps involved in factoring a quadratic equation are: 1. Write the equation in the form ax^2 + bx + c = 0. 2. Find two numbers that multiply to ac (a * c) and add up to b. 3. Rewrite the middle term bx as the two numbers found in step 2. 4. Factor by grouping or using the AC method. 5. Solve for x by setting each factor to zero.

• Subtracting the discriminant from the equation

• Taking the square root of the constant term

Tags

CCSS.HSA-REI.B.4B