PLZ HELP If a vertical parabola opens downward, has its vertex in the fourth quadrant,
and y =ax +bx +c is the equation of this parabola, which of the following
can be true?
a 0, b >0, and c >0
a >0, b 0
a 0, and c >0
a 0, and c 0, b 0
a >0, b >0, and c <0

False

Step-by-step explanation:

A nonlinear function that can be written on the standard form

ax2+bx+c,wherea≠0

is called a quadratic function.

All quadratic functions has a U-shaped graph called a parabola. The parent quadratic function is

y=x2

picture51

The lowest or the highest point on a parabola is called the vertex. The vertex has the x-coordinate

x=−b2a

The y-coordinate of the vertex is the maximum or minimum value of the function.

a > 0                   parabola opens up                    minimum value

picture52

a < 0                    parabola opens down              maximum value

picture53

A rule of thumb reminds us that when we have a positive symbol before x2 we get a happy expression on the graph and a negative symbol renders a sad expression.

The vertical line that passes through the vertex and divides the parabola in two is called the axis of symmetry. The axis of symmetry has the equation

x=−b2a

The y-intercept of the equation is c.

picture54

When you want to graph a quadratic function you begin by making a table of values for some values of your function and then plot those values in a coordinate plane and draw a smooth curve through the points.

Example

Graph

x=x2+2x+1

Make a table of value for some values of x. Use both positive and negative values!

xy = x2 + 2x + 1

-34

-21

-10

01

14

29

316

Graph the points and draw a smooth line through the points and extend it in both directions

picture55

Notice that we have a minimum point which was indicated by a positive a value (a = 1). The vertex has the coordinates (-1, 0)  which is what you will get if you use the formula for the x-coordinate of the vertex

x=−b2a=−22⋅1=−1

and that the line has an y-intercept of (0, 1) which could have been determined from the c-value which is 1.

If you have an absolute value of a that is greater than 1 the parabola will be narrower than the parental quadratic function. And the opposite that if you have a absolute value of a that is less than 1 then the parabola will be wider than the parental quadratic function.

step-by-step explanation:

d? maybe

step-by-step explanation: