Which quadratic function in vertex form can be represented by the graph that has a vertex at (3,-7) and passes through the point (1,-10)?
The quadratic function in vertex form that can be represented by this graph is:
f(x) = (x - 3)^2 - 7
We need to find the value of "a" for the equation by using the point (1, -10):
-10 = (1 - 3)^2 - 7
-10 = (-2)^2 - 7
-10 = 4 - 7
-10 = -3
Since -10 does not equal -3, that means the point (1,-10) does not lie on the graph of the function.
the answer options are
a. y=3/4(x+3)^2+7
b. y=-3/4(x+3)^2-7
c. y=-3/4(x-3)^2-7
d. y=3/4(x-3)^2+7
To find the correct answer, let's substitute the values for the vertex (3, -7) into each of the given answer options and check if they match:
a. y = 3/4(x + 3)^2 + 7
Plugging in (3, -7):
-7 = 3/4(3 + 3)^2 + 7
-7 = 3/4(6)^2 + 7
-7 = 3/4(36) + 7
-7 = 27 + 7
-7 ≠ 34
b. y = -3/4(x + 3)^2 - 7
Plugging in (3, -7):
-7 = -3/4(3 + 3)^2 - 7
-7 = -3/4(6)^2 - 7
-7 = -3/4(36) - 7
-7 = -27 - 7
-7 ≠ -34
c. y = -3/4(x - 3)^2 - 7
Plugging in (3, -7):
-7 = -3/4(3 - 3)^2 - 7
-7 = -3/4(0)^2 - 7
-7 = -3/4(0) - 7
-7 = 0 - 7
-7 = -7 (matches)
d. y = 3/4(x - 3)^2 + 7
Plugging in (3, -7):
-7 = 3/4(3 - 3)^2 + 7
-7 = 3/4(0)^2 + 7
-7 = 3/4(0) + 7
-7 = 0 + 7
-7 ≠ 7
Therefore, the quadratic function in vertex form that can be represented by the graph with a vertex at (3,-7) and passing through the point (1,-10) is:
c. y = -3/4(x - 3)^2 - 7.