Answer:
x=−2
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
−3x−32=−2(5−4x)
−3x+−32=(−2)(5)+(−2)(−4x)(Distribute)
−3x+−32=−10+8x
−3x−32=8x−10
Step 2: Subtract 8x from both sides.
−3x−32−8x=8x−10−8x
−11x−32=−10
Step 3: Add 32 to both sides.
−11x−32+32=−10+32
−11x=22
Step 4: Divide both sides by -11.
−11x
−11
=
22
−11
Answer:
B
Step-by-step explanation:
The graph of g(x) is shifted 4 units up ⇒ answer a
Step-by-step explanation:
Let us revise the translation
- If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)
- If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k
∵ The parent function f(x) = x
∵ g (x) = x + 4
- Substitute x in g(x) by f(x)
∴ g(x) = f(x) + 4
- g(x) is f(x) add by 4
- by using the rule of translation above
∵ g(x) = f(x) + k
∵ k = 4
∴ g(x) is the image of f(x) after translation 4 units up
∴ The graph of g(x) is 4 units above the graph of f(x)
The graph of g(x) is shifted 4 units up
Learn more:
You can learn more about translation in brainly.com/question/2451812
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Answer:
(x - 3)² - 16 = 0
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Subtract 7 from both sides
x² - 6x + 7 = 0 ← in standard form
with a = 1, b = - 6
Given a quadratic in standard form then the x- coordinate of the vertex is
= - 
= - 
= 3
Substitute x = 3 into the equation for y
y = 3² - 6(3) - 7 = 9 - 18 - 7 = - 16 ⇒ (h, k) = (3, - 16)
y = (x - 3)² - 16 = 0
