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STALIN [3.7K]
2 years ago
13

F(x) = -x^2+ 6x -10 write each function in vertex form and give the vertex

Mathematics
1 answer:
Pani-rosa [81]2 years ago
6 0

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 <u>axis of symmtery</u> occurs at x = h. Therefore, the x-coordinate of the vertex is the same as <em>h. </em>

To find the vertex, (<em>h</em>, <em>k</em>), you need to solve for <em>h </em>by using the formula:  h = \frac{-b}{2a}

Plug in the values into the formula:

h = \frac{-b}{2a}

h = \frac{-6}{2(-1)} = 3

Therefore, h = 3.

Next, to find the <em>k</em><em>, </em>plug in the value of<em> </em><em>h</em> 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

<em>a</em> =  determines whether the graph opens up or down, and makes the parent function wider or narrower.

  • If <em>a</em> is positive, the graph opens <u>up</u>.
  • If<em> </em><em>a</em><em> </em>is negative, the graph opens <u>down</u>.

<em>h</em><em> </em>= determines how far left or right the parent function is translated.

<em>k</em> = 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.

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