Regents Exam: Algebra I August 2016 (Problem 19 of 37)

The video tutorial explains how to solve a quadratic equation using two methods: graphing and factoring. The graphing method involves plotting the functions and finding their intersection points, while the factoring method uses decomposition and grouping to solve the equation. Both methods yield the same solutions, demonstrating their effectiveness in solving quadratic equations.

What are the two main methods mentioned for solving the quadratic equation?

• Graphing and factoring

• Substitution and elimination

• Graphing and substitution

• Elimination and factoring

When graphing the functions y = 3x^2 + 10x and y = 8, at which points do they intersect?

• (1, 8) and (-3, 8)

• (3, 8) and (-1, 8)

• (2/3, 8) and (-4, 8)

• (0, 8) and (-2, 8)

What is the purpose of setting the quadratic equation equal to zero before graphing?

• To find the y-intercepts

• To eliminate the constant term

• To find the x-intercepts

• To simplify the equation

What is the first step in the factoring method described in the video?

• Multiply the constant term by the leading coefficient

• Add the constant term to both sides

• Find the greatest common factor

• Set the equation equal to zero

Which integers are used to decompose the linear term in the factoring method?

• 1 and 24

• 2 and 12

• 4 and 6

• 3 and 8

What indicates that the factoring process is on the right track?

• The presence of a common factor

• The equation is simplified

• The terms are grouped correctly

• The leading coefficient is reduced

What are the solutions to the equation after factoring and using the zero product property?

• x = 0 and 2

• x = 3 and -1

• x = 2/3 and -4

• x = 1 and -3