Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
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.
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.
