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

User Ak Sacha
by
8.3k points

2 Answers

4 votes

Answer:

1,8

Explanation:

User Mysteryos
by
7.8k points
1 vote

Answer:

(
(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) )

User Kinkajou
by
8.2k points

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