Question

Determine the number of times the graph of y = 5x² + 7x- 6 intersects the x-axis using two

different methods. The answers from each method should match.

Factoring

Quadratic Formula

Answer 1

Method 1: Factoring

y = 5x² + 7x - 6

= 5x² + 10x - 3x - 6

= 5x(x + 2) - 3(x + 2)

= (5x - 3)(x + 2)

Method 2: Quadratic Formula

x = (-7 ± √(7² - 4 × 5 × -6)) / 2 × 5

= (-7 ± √(49 + 120)) / 10

= (-7 ± √169) / 10

= (-7 ± 13) / 10

x = 4/10 or x = -2

Simplify, we get:

x = 2/5 or x = -2

Therefore, the graph of y = 5x² + 7x - 6 intersects the x-axis at x = 2/5 and x = -2, so it intersects the x-axis twice.