The equation of the new parabola is y = (x - 5)² - 6
Step-by-step explanation:
Let us revise the translation of a function
- 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 equation of the parabola is y = x²
∵ The parabola is shifted down by 6 units
- That means new y = y - k and k = 6
∴ The new y = x² - 6
∵ The parabola is shifted 5 units to the right
- That means the new y = (x - h)² and h = 5
∴ The new y = (x - 5)²
∴ The new equation is y = (x - 5)² - 6
The equation of the new parabola is y = (x - 5)² - 6
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Answer:
y= -2x+3
Step-by-step explanation:
Point slope form= y=mx+b
The m is the slope.
So, we have an incomplete equation right now: y= -2x+b
We want to find b. We can do that by plugging in values for the x and y coordinates. Fortunately, we do have a set of coordinates, (1, 1)!
We plug them in:
1= -2(1)+b
1= -2+b
b=3
So, since we have the slope and the b, also called the y-intercept, we can form an equation!
y= -2x+3
Answer
10 = x
Step-by-step explanation:
The reason for this equation is that it say "5 years less", which we subtract 5, but from what exactly. Well, the next portion of the sentence says "twice Marco's Age" therefore, its 2x so we must subtract 5 from 2x. Later in the problem we are given Yolanda's age so our equation changes to this:
15 = 2x - 5 Now we just solve for x.
15 = 2x - 5 Add 5 to both sides.
+5 + 5
20 = 2x Divide by 2 on both sides
10 = x
As a result, Marcus is 10 years old. Hopefully this makes sense! Feel free to ask any questions!.
PS. This explanation isn't mine found it off another Expert Jose. P -Tutor
Answer:
x=7
Step-by-step explanation:
6x=42
divide 6 on both sides
x=42/6
x=7
