Question

At which of the following points do the two equations f(x)=3x2+5 and g(x)=4x+4 intersect?

Answer 1

1,8

Explanation:

Answer 2

(
`(1)/(3)`,
`(16)/(3)` ) and (1, 8 )

Explanation:

To find the points of intersection equate f(x) and g(x), that is

3x² + 5 = 4x + 4 ( subtract 4x + 4 from both sides )

3x² - 4x + 1 = 0 ← in standard form

(3x - 1)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

3x - 1 = 0 ⇒ 3x = 1 ⇒ x =
`(1)/(3)`

x - 1 = 0 ⇒ x = 1

Substitute these values into either of the 2 functions for corresponding y- coordinates.

Substituting into g(x), then

g(1) = 4(1) + 4 = 4 + 4 = 8 ⇒ (1, 8 )

g(
`(1)/(3)` ) =
`(4)/(3)` + 4 =
`(16)/(3)` ⇒ (
`(1)/(3)`,
`(16)/(3)` )