Mathematics, 04.01.2020 19:31 MegRasmussen31

Formulate the quadratic function that contains the points (-1,2), (0,-1) and (2,5).

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The idea here is to take all three of those points and sub them into the general form of the quadratic equation and solve 3 equations by doing them 2 at a time. The general form is y = ax^2 + bx + c. If we set up the first two equations together using the x and y coordinates of the first 2 coordinates given, the system looks like this: 2 = a(-1)^2 + b(-1) + c
-1 = a(0)^2 +b(0) + c
Solving the second one gives you that c = -1, so we already know c. Solving the first equation we get 2 = a - b - 1, or 3 = a - b, subbing in a -1 for c. The next equation, using the last coordinate, looks like this: 5 = a(2)^2 + b(2) - 1 and
5 = 4a + 2b - 1 and 6 = 4a + 2b. Now we have these two equations left:
3 = a - b and 6 = 4a + 2b. Solve the first equation for b to get it in terms of a only: b = a - 3. Now sub in that b value for b in the second equation:
6 = 4a + 2(a - 3) and 6 = 6a - 6 and 12 = 6a so a = 2. Now we have a and c. Sub in the a value of 2 into b = a - 3 to get 3 = 2 - b. Solve for b to get that b = -1. So our equation in the end finally is y = 2x^2 - x - 1.

Answer from: Quest

what is the rest of the question? ?

Answer from: Quest

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem, $a^2+b^2=c^2$

in this case, a=b since isocolese triangle so we get

$2a^2=c^2$ or $a=\frac{c}{\sqrt{2}}$

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

$(x-x_a)^2+(y-y_a)=(\frac{c}{\sqrt{2}})^2$ and

$(x-x_b)^2+(y-y_b)^2=(\frac{c}{\sqrt{2}})^2$ intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough

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Formulate the quadratic function that contains the points (-1,2), (0,-1) and (2,5)....