Answer:
Step A. 3(m - 2) + 2(m - 2) and 5(m - 2) are equivalent expressions.
Step-by-step explanation:
Step B. If you calculate 3(m - 2) + 2(m - 2) you will see it will equal to 5(m - 2) therefore, they are equal.
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To find f(-2), substitute (-2) into x of the function f(x) = 4x^2-2
We get, f(-2) = 4(-2)^2 - 2
= (4*4)-2 = 16-2 = 14
Therefore, f(-2)=14.
X=7
7x-2=5x+12
+2. +2
7x=5x+14
-5x -5x
2x=14
÷2 ÷2
x=7
Y = -(1/2)(x-2)² +8
Re write it in standard form:
(y-8) = -1/2(x-2)² ↔ (y-k) = a(x-h)²
This parabola open downward (a = -1/2 <0), with a maximum shown in vertex
The vertex is (h , k) → Vertex(2 , 8)
focus(h, k +c )
a = 1/4c → -1/2 = 1/4c → c = -1/2, hence focus(2, 8-1/2) →focus(2,15/2)
Latus rectum: y-value = 15/2
Replace in the equation y with 15/2→→15/2 = -1/2(x-2)² + 8
Or -1/2(x-2)² +8 -15/2 = 0
Solving this quadratic equation gives x' = 3 and x" = 2, then
Latus rectum = 5
