Exploring Methods to Solve Quadratic Equations

What are the four main methods for solving quadratic equations?

• Graphing, substitution, elimination, and matrices

• Factoring, square root, completing the square, and the quadratic formula

• Division, multiplication, addition, and subtraction

• Derivatives, integrals, limits, and continuity

Tags

CCSS.HSA-REI.B.4B

What is the first step in solving quadratic equations by factoring?

• Find the discriminant

• Calculate the vertex

• Rewrite the equation in standard form

• Determine the axis of symmetry

Which pair of factors of -18 adds up to the middle term of 3?

• -9 and 2

• 9 and -2

• -6 and 3

• 6 and -3

Tags

CCSS.HSA-REI.B.4B

When solving by taking the square root, why must we consider both positive and negative roots?

• Because it's a convention in mathematics

• To ensure the solution set is complete

• Because both roots can potentially satisfy the original equation

• Both A and B are correct

Tags

CCSS.HSA-REI.B.4B

What must the coefficient of x^2 be to complete the square?

• Any non-zero number

• 0

• -1

• 1

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CCSS.HSA-REI.B.4B

What is the purpose of completing the square in solving quadratic equations?

• To find the equation's discriminant

• To simplify the equation for graphing

• To transform the equation into a perfect square trinomial

• To determine the equation's coefficients

What is the standard form of a quadratic equation?

• ax + bx^2 = c

• a(x - h)^2 + k = 0

• ax^2 + bx + c = 0

• ax^2 + bx = c

Tags

CCSS.HSA-REI.B.4B

In the quadratic formula, what do the letters a, b, and c represent?

• Intercepts of the graph of the quadratic equation

• Vertices of the parabola represented by the quadratic equation

• Solutions of the quadratic equation

• Coefficients of the quadratic equation in standard form

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CCSS.HSA-REI.B.4B

What is the quadratic formula?

• x = (-b ± sqrt(b^2 - 4ac)) / 2a

• x = (b ± sqrt(b^2 + 4ac)) / 2a

• x = (b ± sqrt(b^2 - 4ac)) / 2a

• x = (-b ± sqrt(b^2 - 2ac)) / 2a

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CCSS.HSA-REI.B.4B

Why is the quadratic formula useful?

• It calculates the discriminant

• It provides an exact solution for any quadratic equation

• It is the only method to solve quadratic equations

• It simplifies the process of graphing quadratic equations

Tags

CCSS.HSA-REI.B.4B