# How do you find the axis of symmetry, and the maximum or minimum value of the function #y=x^2+3x-5#?

The axis of symmetry is

The vertex is

Given:

where:

The formula to find the axis of symmetry:

Plug in the known values.

Simplify.

graph{y=x^2+3x-5 [-16.02, 16.01, -8.01, 8.01]}

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

The axis of symmetry of the function ( y = x^2 + 3x - 5 ) is given by the formula ( x = -\frac{b}{2a} ), where ( a ) is the coefficient of the quadratic term and ( b ) is the coefficient of the linear term. In this case, ( a = 1 ) and ( b = 3 ), so the axis of symmetry is ( x = -\frac{3}{2} ).

To find the maximum or minimum value of the function, we can evaluate the function at the axis of symmetry. Substitute ( x = -\frac{3}{2} ) into the function to get ( y = (-\frac{3}{2})^2 + 3(-\frac{3}{2}) - 5 = -\frac{17}{4} ).

Therefore, the axis of symmetry is ( x = -\frac{3}{2} ), and the function has a maximum value of ( y = -\frac{17}{4} ) at that point.

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.

- The length of a rectangle is 5 yd less than double the width, and the area of the rectangle is 52 yd^2 . How do you find the dimensions of the rectangle?
- What is the equation of the axis of symmetry for the graph of #f(x) = 2x^2 + x - 3#?
- How do you solve #-3x^2-12=14x# by completing the square?
- How do you solve #x^2-2x+9=0#?
- How do you use the quadratic formula to find both solutions to the quadratic equation #(2y - 3) (y + 1) = 5#?

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