# How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #y=-x^2+6x-2#?

Maximum

Axis of symmetry

Given -

#y=-x^2+6x-2#

Vertex -

#x=(-b)/(2a)=(-6)/(2 xx (-1))=(-6)/(-2)=3#

#y=-(3)^2+6(3)-2=-9+18-2=18-11=7#

#(3, 7)#

Axis of symmetry -

#x=3#

How to graph?

After finding the vertex, take a few points on either side of

Find the corresponding y values.

Graph them

By signing up, you agree to our Terms of Service and Privacy Policy

To find the axis of symmetry of a quadratic function in the form (y = ax^2 + bx + c), use the formula: (x = -\frac{b}{2a}).

For the given function (y = -x^2 + 6x - 2), (a = -1) and (b = 6).

Substitute these values into the formula: (x = -\frac{6}{2(-1)} = -\frac{6}{-2} = 3).

So, the axis of symmetry is (x = 3).

To find the vertex, substitute (x = 3) into the function: (y = -(3)^2 + 6(3) - 2 = -9 + 18 - 2 = 7).

Thus, the vertex is ( (3, 7)).

Since the coefficient of (x^2) is negative, the parabola opens downwards, and the vertex represents the maximum value of the function.

So, the maximum value of the function is (y = 7), which occurs at (x = 3).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you solve #-4x^2 + 5x + 6 = 0 #?
- How do you find the value of the discriminant and determine the nature of the roots #-4m^2-4m+5#?
- How do you solve #3x^2-12=0# using the quadratic formula?
- How do you find the domain, find where f is increasing, vertex, intercepts, maximum of #f(x)=-(x-2)^2+1#?
- How do you identify the important parts of #y= -4x^2# to graph it?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7