Question

Consider the parabola given by the equation: f ( x ) = − 2 x 2 − 14 x − 1 Find the following for this parabola: A) The vertex: (-3.5,23.5) Correct B) The vertical intercept is the point (0,-1) Correct C) Find the coordinates of the two x intercepts of the parabola and write them as a list, separated by commas: (1/2,0),(-7,0) Incorrect It is OK to round your value(s) to to two decimal places.

Answer 1

a) (-3.5;23.5)

b) (0,-1)

c) (-0.07;0) and (-6.93;0)

Explanation:

f(x) = − 2x² − 14 x − 1

a) vertex

b) vertical intercept

c) 2 x intercept (round to two decimal places)

a) Vertex (-b/2a; -Δ/4a)

a = -2 | b = -14 | c = -1

xv = -(-14)/2.(-2) = 14/-4 = -3.5

Δ = b² - 4ac = (-14)² - 4.(-2).(-1) = 196 - 8 = 188

yv = -188/4.(-2) = -188/-8 = 23.5

Vertex(-3.5;23.5)

b) vertical intercept ⇒ x = 0

f(0) = -2.0² - 14.0 - 1 = -1

vertical intercept: (0,-1)

c) x intercept ⇒ roots

Δ = b² - 4ac = (-14)² - 4.(-2).(-1) = 196 - 8 = 188

√Δ = √188 = 13.71

x = -(-14) ± 13.71/2.(-2) = 14 ±13.71/-4

x' = 14 -13.71/-4 = -0.07

x" = 14 + 13.71/-4 = -6.93

So, the x intercept points are (-0.07;0) and (-6.93;0)