Work out the coordinates of the points of intersection of the graphs y= 4x^2+8x+3 and y=x+5
Answer (,) and (,)

Step-by-step explanation:

The point of intersection occurs when the two graphs have equal values of  x and  y at the same time. There is only one solution, because two straight lines can only intersect once.

Answer :

(- 2, 3 ) and (, )

Step-by-step explanation:

Given the 2 equations

y = 4x² + 8x + 3 → (1)

y = x + 5 → (2)

Substitute y = 4x² + 8x + 3 into (2)

4x² + 8x + 3 = x + 5 ( subtract x + 5 from both sides )

4x² + 7x - 2 = 0 ← in standard form

(x + 2)(4x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

4x - 1 = 0 ⇒ 4x = 1 ⇒ x =

Substitute these values into (2) for corresponding values of y

x = - 2 : y = - 2 + 5 = 3 ⇒ (- 2, 3 )

x = : y = + 5 = ⇒ (, )