The standard equation of a parabola is y=ax2 + 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=ax2 + bx + c
- (5)=a(0)2 + b(0) + c.
For the vertex values, you must rearrange the standard equation a little bit.
y=ax2 + 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 (x2 + 4x + 4) + 1
- y= ax2 + 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:
ax2 = ax2 --> a=a (No new value is learned)
4a + 1 = c
- 4a + 1 = (5)
- a= 1
- 4a= b
- 4(1) = b
You know have all the values. a= 1, b= 4 and c=5
If you plug these values into the standard parabolic equation, y=ax2 + bx + c, and simplify, you successfully reconstruct the equation.
y= (1)x2 + (4)x + (5)
y= x2 + 4x + 5
Hope this helps :)
*NOTE: Thank you, Natalia D. for catching my error. My response has now been edited to the correct version.*