Question

Included in the figure is the equation of the parabola y = x ^ 2 + 4x + 5. The point N is the vertex of the parabola. Write the equation of the line MN.

Answer 1

y = 3x + 3

Explanation:

y = -x² + 4x + 5

→ Find the vertex

- ( x - 2 )² + 4 + 5 ∴ vertex = ( 2 , 9 )

→ Find the intersection with the x axis

- ( x - 5 ) ( x + 1 ) ∴ ( - 1 , 0 )

→ Find the gradient of the 2 point

( 0 - 9 ) ÷ ( -1 - 2 ) = 3

→ Write into y = mx + c format

y = 3x + c

→ Substitute in a coordinate pair

0 = -3 + c ∴ c = 3

→ Rewrite into y = mx + c

y = 3x + 3