Y=-x^2+6x-4
Find the Axis of Symmetry and the Vertex, Also solve the whole equation.

1. Axis of symmetry: x = 3

2. Vertex: (3,5)

3. Solution of the equation:

Explanation:

1. Equation:

2. Axis of symmetry:

That is the equation of a parabola, whose standard form is:

Where:    

The axis of symmetry is the vertical line with equation:

Substitute  

Thus, the axis of symmetry is:

3. Vertex

The x-coordinate of the vertex is equal to the axys of symmetry, i.e x = 3.

To find the y-xoordinate, substitute this value of x into the equation for y:

Therefore, the vertex is (3, 5)

4. Find the x-intercepts

The x-intercepts are the roots of the equation, which are the points wher y = 0.

Use the quadratic equation:

5. Find the y-intercept

The y-intercet is the value of y when x=0:

idk idk idk idk idk

step-by-step explanation:

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.