Question

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

Answer 1

Answer:

($\frac{1}{3}$, $\frac{16}{3}$ ) and (1, 8 )

Step-by-step 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 = $\frac{1}{3}$

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($\frac{1}{3}$ ) = $\frac{4}{3}$ + 4 = $\frac{16}{3}$ ⇒ ($\frac{1}{3}$, $\frac{16}{3}$ )