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Sagot :
Answer:
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!
x y = x2 + 2x + 1
-3 4
-2 1
-1 0
0 1
1 4
2 9
3 16
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.
The vertical parabola opens downward, has its vertex in the fourth quadrant, and y = ax + bx +c is the equation of this parabola given conditions none of them is true.
A nonlinear function that can be written on the standard form
[tex]ax^{2} + bx +c = 0 where (a\neq 0)[/tex]
This called a quadratic function.
All quadratic functions has a U-shaped graph called a parabola. The parent quadratic function is'
[tex]y = x^{2}[/tex]
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 value maximum or minimum of the function.
a > 0 parabola opens up minimum value
a < 0 parabola opens down maximum value
A rule of thumb reminds us that when we have a positive symbol before 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.
[tex]XY = x^{2} +2X +1[/tex]
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.
[tex]x = x^{2} +2x+1[/tex]
Make a table of value for some values of x. Use both positive and negative values!
This is the points lies on parabola
- -3 4
- -2 1
- 2 9
- 3 16
Graph the points and draw a smooth line through the points and extend it in both directions.
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.
For more information about basics of parabola click the link given below .
https://brainly.com/question/13053904.
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