For the following function, find a. the equation of the axis of symmetry and b. the vertex of its graph.
f(x)=−x2+2x−4
incorrect
@ Anonymous, don't just post answers, especially if they are wrong.
A. x=-1
B. (-1,-5)
To find the equation of the axis of symmetry and the vertex of the graph of the given function, we can use the formula:
Axis of Symmetry = -b/2a
For the given function f(x) = -x^2 + 2x - 4, we can see that a = -1 and b = 2.
a. Equation of the Axis of Symmetry:
Using the formula, we substitute the values of a and b into the equation:
Axis of Symmetry = -2 / (2 * -1)
Axis of Symmetry = -2 / -2
Axis of Symmetry = 1
Therefore, the equation of the axis of symmetry is x = 1.
b. Vertex of the Graph:
To find the vertex, we substitute the value of the equation of the axis of symmetry (x = 1) into the original function to find the corresponding y-coordinate.
f(1) = -(1)^2 + 2(1) - 4
f(1) = -1 + 2 - 4
f(1) = -3
So, the vertex is the point (1, -3).
Therefore, the equation of the axis of symmetry is x = 1 and the vertex of the graph is (1, -3).