Max/min, doman, range, end behavior, interval of increase and decrease

Question

2x^2 + 3x - 2

Find the Maximum and Minimum Value for this quadratic

Find the range and domain for this quadratic

Find the end behavior for this quadratic

Find the interval of increase for this quadratic

FInd the interval of decrease for this quadratic

show your work

Answer 1

The quadratic function f (x ) = 2x ² +3x -2

Compare the standard form of parabola y = ax² + bx + c.

a = 2 , b = 3 , c = -2.

Axis of symmetry x = -b /2a

x  = -3/4

Substitute the x  value in y  = 2x ² + 3x -2.

y  = -25/8

Vertex of parabola (x , y ) = (-3/4 , -25/8)

The quadratic function is even  degree polynomial with positive leading coefficient,

There fore the end behaviour on both sides is up.

The quadratic maximum value is infinity.

To find the minimum it is simply lowest y coordinate.Since we know the vertex is minimum or maximum value of quadratic function.

In this case parabola opens up so the minimum value is -25/8.

The function f (x ) = 2x ² + 3x - 2 is a quadratic function or parabola function.There are no rational or radical expressions, so there is nothing that will restrict the domain. Any real number can be used for x to get a meaningful output.

Domain is all real numbers.

In the minimum value y = -25/8 ,so the graph of parabola cannot be lower than -25/8.

Range of function is

We alredy know the graph turning at vertex.It is decreasing to left of the vertex and increasing on the right.

If a > 0, then we have a parabola that open up
So vertex is minimum point
Function decreases on interval (-∞, -b /2a)
Function increases on interval (-b /(2a ), ∞)

Decreasing interval (-∞,-3/4)

Increasing interval (-3/4,∞).