Answer:
f(x) = (x + 4)² - 3
Step-by-step explanation:
The equation of a quadratic function in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given
f(x) = x² + 8x + 13
To obtain f(x) in vertex form use the method of completing the square
add/ subtract (half the coefficient of the x- term)² to x² + 8x
f(x) = x² + 2(4)x + 16 - 16 + 13
f(x) = (x + 4)² - 3 ← in vertex form
Answer:
Step-by-step explanation:
We can use the quadratic formula or factor, This looks hard to factor so we should use the quadratic formula.
ax^2 + bx + c
so
a=4
b=-9
c=2
you can try it by hand or use this:
https://www.calculatorsoup.com/calculators/algebra/quadratic-formula-calculator.php
you get x=2 and x=0.25 these are the x intercepts (where Y is zero and where the graph crosses the x axis)
so mark x=2 and x=0.25 with a dot on a number line and you can draw a straight line between them since that is the part of the graph that is below the x axis (because the equation has <0) it is a positive parabola because the "a" value is positive and the presence of a "b" value means part of the graph will be below the x axis
Answer:
Area shaded portion = 16/3 π - 8√3
Step-by-step explanation:
The shaded portion consists of 2 equal segment
∵ Two circles have the same radii = 4
∵ The the length of the common chord of the two circles = 4
∴ The central angle of each segment = π/3 (60° equilateral Δ)
∵ Area segment = area sector - area Δ
∵ Area sector = 1/2 r²Ф = 1/2 × (4)² × π/3 = 8/3 π
∵ Area Δ = 1/4 s² √3 = 1/4 × (4)² × √3 = 4√3
∴ Area segment = 8/3 π - 4√3
∴ Area shaded portion = 2(8/3 π - 4√3) = 16/3 π - 8√3
