The graph of y=ax^2+bx+c is translated by the vector (4 5). The resulting graph is y=2x^2-13x+21.Find the values of a,b and c are constants to be found.
To find the values of a, b, and c, we need to compare the given equation, y = 2x^2 - 13x + 21, with the general equation, y = ax^2 + bx + c.
By comparing the coefficients of the corresponding terms on both sides of the equation, we can determine the values of a, b, and c.
1. Comparing the coefficients of x^2:
We have 2x^2 on the right side, which means that the value of a is 2.
2. Comparing the coefficients of x:
We have -13x on the right side, which means that the value of b is -13.
3. Comparing the constant terms:
We have 21 on the right side, which means that the value of c is 21.
Therefore, the values of a, b, and c are:
a = 2
b = -13
c = 21