Answer:
Vertex form: f(x) = – (x – 3)² – 1
vertex: (3, -1)
Step-by-step explanation:
Given the quadratic function, f(x) = -x²+ 6x -10:
where a = -1, b = 6, and c = -10
The vertex of a parabola is the point at which the parabola intersects the axis of symmetry. The axis of symmtery occurs at x = h. Therefore, the x-coordinate of the vertex is the same as h.
To find the vertex, (h, k), you need to solve for h by using the formula: [tex]h = \frac{-b}{2a}[/tex]
Plug in the values into the formula:
[tex]h = \frac{-b}{2a}[/tex]
[tex]h = \frac{-6}{2(-1)} = 3[/tex]
Therefore, h = 3.
Next, to find the k, plug in the value of h into the original equation:
f(x) = -x²+ 6x -10
f(x) = -(3)²+ 6(3) -10
f(x) = -1
Therefore, the value of h = -1.
The vertex = (3, -1).
Now that you have the value for the vertex, you can plug these values into the vertex form:
f(x) = a(x - h)² + k
a = determines whether the graph opens up or down, and makes the parent function wider or narrower.
h = determines how far left or right the parent function is translated.
k = determines how far up or down the parent function is translated.
Plug in the vertex, (3, -1) into the vertex form:
f(x) = – (x – 3)² – 1
This parabola is downward-facing, with its vertex, (3, -1) as its maximum point on the graph.
