Whatt is the equationn in vertex form whose graph has a maxium pointt att (-2,6) and passes through (1,-5)?
To find the equation of a quadratic function in vertex form, which represents a parabola, you need the vertex coordinates and one other point on the graph.
In this case, we are given the vertex as (-2, 6) and a point on the graph as (1, -5).
The vertex form of a quadratic equation is given as follows:
y = a(x - h)^2 + k
where (h, k) represents the vertex coordinates. Substituting the given vertex into the equation, we get:
y = a(x - (-2))^2 + 6
y = a(x + 2)^2 + 6
Now, we can use the given point (1, -5) to solve for the coefficient 'a'. Substituting the coordinates of the given point into the equation, we get:
-5 = a(1 + 2)^2 + 6
-5 = a(3)^2 + 6
-5 = 9a + 6
To solve for 'a', we can subtract 6 from both sides:
-11 = 9a
Now, divide both sides by 9 to isolate 'a':
a = -11/9
Now we have the value of 'a', we can substitute it back into the equation to get the final equation in vertex form:
y = (-11/9)(x + 2)^2 + 6
So, the equation in vertex form whose graph has a maximum point at (-2,6) and passes through (1,-5) is y = (-11/9)(x + 2)^2 + 6.