The parabola \(y = ax^2 + bx + c\) is graphed below. Find \(a+b+c\). (The grid lines are one unit apart.)

Guest Jun 30, 2020

#1**0 **

Using the graphing equation: y = a(x - h)^{2} + k where (h, k) is the vertex.

The vertex of this parabola occurs at (2, 1) ---> y = a(x - 2)^{2} + 1

It rises, so that the value of a is positive.

It has no stretching or contracting so the value of a is 1.

The equation is: y = 1(x - 2)^{2} + 1 or y = (x - 2)^{2} + 1.

Now, multiply this out and simplify ...

geno3141 Jun 30, 2020

#4**+1 **

Notice that the curve goes through the following three points (you could choose any three, but these are easy ones):

(0, 5) (2, 1) and (4, 5)

This allows you to set up the following three equations:

5 = a*0^{2} + b*0 + c or simply c = 5

1 = a*1^{2} + b*1 + c or a + b = -4 ...(1)

5 = a*4^{2} + b*4 + c or 16a + 4b = 0 ...(2)

You could solve equations (1) and (2) for a and b if you wish; however, since you are only asked for a + b + c you could simply use the value of a + b from (1) together with the value for c.

Alan Jul 1, 2020