Answer:
The parent function is f(x) = |x|
Step-by-step explanation:
Option 1 and 4 are not absolute value, and option 3 has a number before it making it changed.
30 minutes = 5 puzzles
60 minutes = 10 puzzles
90 minutes = 15 puzzles
She will solve 15 puzzles in an hour and 30 minutes
Given the vertex, (-4, 3):
We can use the quadratic function in vertex form, f(x) = a(x - h)^2 + k where:
(h, k) = vertex
a = determines whether the graph opens up or down, and makes the parent function wider or narrower.
* If a is positive, the graph opens up.
* If a is negative, the graph opens down.
h = determines how far left or right the parent function is translated.
k = determines how far up or down the parent function is translated.
Now that we defined each variable in the vertex form, we can plug in the values of the vertex (-4, 3) into the equation:
f(x) = a(x - h)^2 + k
f(x) = a(x + 4)^2 + 3
To solve for the value of “a”, we must choose another point from the graph. The y-intercept of the parabola happens to be (0, 19), so we’ll use its values to solve for “a”:
19 = a(0 + 4)^2 + 3
19 = a(4)^2 + 3
19 = a(16) + 3
Subtract 3 from both sides:
19 - 3 = a(16) + 3- 3
16 = 16a
Divide both sides by 16:
16/16 = 16a/16
1 = a
The value of a = 1. Since it is a positive number, then it confirms that the parabola opens upward.
Therefore, the quadratic function in vertex form is:
f(x) = (x + 4)^2 + 3
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Answer:
No, Mia is not correct, the answer is -2.
Step-by-step explanation:
First we are going to use the distributive Property.
Step 1: 2(0.75+0.4). multiply the 2 out. .75m x 2=1.5m and 2 x .4= .8.
We get 1.5m+.8, so 2(0.75+0.4)=1.5m+.8
Now we are going to distribute on the oher side. 4(.5m-.8)
4x .5m=2m and 4x.8=3.2. Keep the sign the same and we get 2m-3.2, so 4(.5m-.8)=2m-3.2
We put this into the new equation to get 1.5m+.8+7.8=-6.4m+2m-3.2
Step 2: combine like terms
.8+7.8= 8.6 and -6.4m +2m =-4.4m
Plug that into our equation and we get 1.5mn+8.6=-4.4m-3.2
Step 3: Switch the sides
Bring -4.4m to the other side to get 1.5m+4.4m=5.9m
One side is 5.9m
We bring 8.6 to the other side to get -8.6. now we do -3.2-8.6=-11.8.
Our new equation is 5.9m=-11.8
divide by 5.9 on both sides to get our answer of
m=-2
