Melissa J. answered • 05/16/13

Science (specializing in Chemistry) and Writing Tutor

The standard equation of a parabola is y=ax^{2} + bx + c. In this problem, you are given the coordinates of the vertex (-2,1) and the y-intercept (0,5). The point of this question is to find out the values of "a", "b" and "c".

If you plug in the values of the y-intercept (given) into the standard equation...

- y=ax
^{2}+ bx + c - (5)=a(0)
^{2}+ b(0) + c. - c=5

For the vertex values, you must rearrange the standard equation a little bit.

y=ax^{2} + bx + c

y= a(x-h)^{2 }+ k with the vertex being (h,k)

Now, plugging in the vertex values...

- y= a( x- (-2))
^{2}+ 1 - y= a (x
^{2}+ 4x + 4) + 1 - y= ax
^{2}+ 4ax + 4a + 1

Recalling the standard equation of the parabola, you can match up the components of the equation according to the powers of x:

ax^{2 = }ax^{2 }--> a=a (No new value is learned)

4a + 1 = c

- 4a + 1 = (5)
- a= 1

4ax= bx

- 4a= b
- 4(1) = b
- b=4

You know have all the values. a= 1, b= 4 and c=5

If you plug these values into the standard parabolic equation, y=ax^{2} + bx + c, and simplify, you successfully reconstruct the equation.

y= (1)x^{2} + (4)x + (5)

**y= x ^{2} + 4x + 5**

Hope this helps :)

*NOTE: Thank you, Natalia D. for catching my error. My response has now been edited to the correct version.*

Nataliya D.

If (-2, 1) "plug in" into y = x

^{2}+ 2x + 51 ? (-2)

^{2}+ 2(-2) + 51 ? 5

05/16/13