What is the y-value of the vertex of the function f(x)=-(x+8)(x-14)? 3 6 112 121
2 answers:
Answer:
121
Step-by-step explanation:
Given
f(x) = - (x + 8)(x - 14) ← expand factors using FOIL
= - (x² - 6x - 112) ← distribute by - 1
= - x² + 6x + 112
Given a quadratic in standard form. y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
= -
f(x) = - x² + 6x + 112 ← is in standard form
with a = - 1 and b = 6, thus
= -
= 3
Substitute x = 3 into f(x) for corresponding value of y
f(3) = - (3)² + 6(3) + 112 = - 9 + 18 + 112 = 121
vertex = (3, 121 ) ← with y = 121
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Answer:
Step-by-step explanation:
Given
sinΘ = =
Then the hypotenuse = 5 and one leg of the right triangle is 3
Using Pythagoras' identity to find the second leg (x)
x² + 3² = 5²
x² + 9 = 25 ( subtract 9 from both sides )
x² = 16 ⇒ x = 4
cosΘ = =