Answer:
y = 4x² -3x +5
Step-by-step explanation:
It can be helpful to plot the points on a graph. The curve through them opens upward, so you know <em>the first two answer choices are incorrect</em>.
<em>Looking at the location of the vertex</em>
The points (-1, 12) and (2, 15) have nearly the same y-value, so the vertex of the parabola will be nearly halfway between those points, at about ...
... x = (-1 +2)/2 = 1/2
Because the point at (2, 15) has a slightly higher y-value, you know it is farther from the vertex, so the vertex will be at an x-value that is less than 1/2.
For quadratic ...
... y = ax² +bx +c
the vertex is found at
... x = -b/(2a)
For the 3rd choice, this is x = -(-4)/(2·3) = 2/3. This is higher than 1/2, so we can eliminate this choice, too.
Only the 4th choice remains. (It passes the vertex location test: x = -(-3)/(2·4) = 3/8 < 1/2.)
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There are some other ways to solve this problem, too.
- try the given points in the given equations. The +5 as a constant of all of them tell you that all will work for x=0. Both of choices 3 and 4 work for x=-1, so we have to try x=2. Choice 3: 3·2² -4·2 +5 = 9, not 15. Choice 4: 4·2² -3·2 +5 = 15. So Choice 4 is the answer.
- write equations for a, b and solve them. a(-1)² +b(-1) +5=12; a(2)² +b(2)+5=15. or a-b=7, 2a+b=5 in standard form. Adding these gives 3a=12, so a=4 and Choice 4 is the answer.
- use a graphing calculator to write the quadratic regression formula from the three points. This result is shown in the attachment. The (a, b, c) = (4, -3, 5) correspond to Choice 4.
Answer:
The answer is A
Step-by-step explanation:
The first thing to do is see which two lengths of EF and FG equals EG which is 23. If you add together B's options you get -12 and if you add C's options, you get 77. So that leaves us with the options of A and D. From there, just plug in each value of x and see which one gets you the right values. Hope this helps
The answer is D because when u divide it
Well the formula for a triangle is base(b) times height(h) divided by 2.
Answer:
Danny: y-=.75x+20
Avery: y=1.25x+18
Step-by-step explanation:
To write a system of equations, it usually equals y=mx+b. Since Danny and Avery both earn the set monthly allowance of 20 and 18 dollars respectively, those numbers go on the variable b since it's a set amount and they start off with that amount of money if they weren't nice to their mom at all.
Since we are trying to find the overall amount of money, let y=total money a child earns every month and x=how many times the child is nice to their mother.
The extra .75 cents Danny earns go under the variable m because it is dependent on how many times he is nice to his mom. Along with Avery.