Answer:
a) (-3.5;23.5)
b) (0,-1)
c) (-0.07;0) and (-6.93;0)
Step-by-step 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)
