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.

see the question there is translation

To find the values of a, b, and c, we need to compare the given equation of the translated graph, y = 2x^2 - 13x + 21, with the general equation of a quadratic function, y = ax^2 + bx + c.

When the graph is translated by the vector (4, 5), the x-coordinate of each point is increased by 4, and the y-coordinate is increased by 5.

So, we have the following relationship between the original graph and the translated graph:

y = ax^2 + bx + c (original graph)
y + 5 = 2(x + 4)^2 - 13(x + 4) + 21 (translated graph)

Now, let's expand and compare the two equations:

Original graph: y = ax^2 + bx + c

Expanded translated graph:
y + 5 = 2(x^2 + 8x + 16) - 13x - 52 + 21
y + 5 = 2x^2 + 16x + 32 - 13x - 31
y + 5 = 2x^2 + 3x + 1

Comparing the two equations, we can determine the values of a, b, and c:

a = 2
b = 3
c = 1

Therefore, the values of a, b, and c are 2, 3, and 1, respectively.

To solve this problem, we need to use the concept of translation of a graph. When a graph is translated by a vector (h, k), every point on the graph is shifted horizontally by h units and vertically by k units. In this case, the given graph is translated by the vector (4, 5), which means every point on the graph is shifted 4 units to the right and 5 units up.

We are also given the resulting graph, which is represented by the equation y = 2x^2 - 13x + 21. From this equation, we can determine the values of a, b, and c by comparing it with the general equation y = ax^2 + bx + c.

Comparing the equations, we have:

a = 2
b = -13
c = 21

Therefore, the values of a, b, and c are 2, -13, and 21, respectively.

a=2

b=-13
c=21