Quadratics Standard Form

By: Vikash Singh

Standard Form Equation:

y=ax^2+bx+c

Learning Goals:

1. I learned to use the Quadratic Formula to find the x-intercepts.

2. I learned how to use the Discriminant to find how many x-intercepts a quadratic function has.

3. I learned how to graph a Quadratic Function using the Quadratic Formula.

4. I learned how to Complete The Square to find the Maximum/Minimum value of the quadratic and its' vertex.

Summary:

  • Standard for Equation: y=ax^2+bx+c.
  • the value of a gives you the shape and direction of opening.
  • the value of c is the y-intercept.
  • Solve using the quadratic formula, to get the x-intercepts.
  • MAX or MIN? Complete the square to get vertex form.
  • Discriminant Formula: x=(b^2 - 4ac).
  • In order to find the x-intercepts use the Quadratic Formula.

Quadratic Formula:

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Completing The Squares:

  • Transforms a standard equation into vertex form to get the vertex and the maximum/minimum value.
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The Discriminant:

  • The discriminant Formula is used to identify the number of c-intercepts in a quadratic function
  • Given that a,b and c are rational numbers, they are needed to determine the discriminant.
  • Discriminant equation: x=(b^2-4ac)
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Graphing Standard Form:

  1. Find the X-intercepts using the quadratic formula.
  2. Find the vertex using AOS=(r+s)/2 to find the x-value and then sub it into the original equation to solve for y.
  3. Plot the points that was received from the data to form a parabola.

Here Is a Video to Help You Understand Further How to Complete the Square:

Completing the square

Standard Form Example:

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Here is an Example of Completing The Square:

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Reflection:

  • Quadratics has been a very interesting and fun unit to learn this year. Quadratics compares to many things needed to be done throughout the world.
  • During this unit I have made some mistakes, but i practiced and will keep practicing to get better. I was able to succeed and understand the whole unit and apply each of the concepts of the quadratics unit.

Some Formulas in Quadratics:

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Connections:

  1. Vertex Form to Graphing:
  • When you have the vertex form of an equation, you are able to identify the vertex and plot the graph.
  • When you have plotted the vertex you can you can use the step pattern to get both sides.
2. Vertex Form to Standard Form:
  • You must expand vertex form in order to achieve the standard form.
  • you can also complete the square from standard form to get to vertex form,
3. Standard Form to Graphing:
  • In standard form the c value gives you the y intercept.
  • Transform your standard form equation to vertex form by completing the square, and that will give you the vertex.
  • Plot the vertex and use the vertex as well as the step pattern to plot your quadratic.
4. Factored Form to Graphing:
  • When an equation is in factored Form you can easily find the x-intercepts and the a value.
  • You can use the x-intercepts to find the vertex.
  • Then plot all points and continue to graph.
5. Factored to Standard Form:
  • In factored Form once the two x-intercepts are found by factoring, find the vertex by using AOS, and subbing x into the original equation for y.
  • In standard form once the two x intercepts are found, find the vertex by using AOS, and subbing x into the original equation for y.
6. All Forms Connecting Together. (Vertex, Standard, Factored)
  • To find the y-intercept for all of these forms, when x=0 the y-intercept is able to be found.
  • The y intercept is written as (0,y)

Assessment: Standard Form Unit Test

  • This assessment strengthened my understanding that their are multiple ways to come to a solution.
  • I made sure that i was always right by checking my work by completing the square to achieve the vertex of the equation.
  • For the vertex, i did it b using the quadratic formula to find the x-intercepts then go along to find the vertex.
  • This helped me to realize there are man ways to solve problems.

This Video Shows the Introduction into Standard Form from Linear Equations:

Standard form for linear equations | Algebra I | Khan Academy

Key Terms:

1.Minimum: the lowest point on a parabola that opens up

2.Maximum: the highest point on a parabola that opens down

3.the x-part of the vertex: -b/2a

4.parabola: the graph of a quadratic function

5.standard form of a parabola: y=ax^2 + bx + c

6.axis of symmetry: the line of reflection for a parabola

7.y-intercept: the point where the graph intersects the y-axis

8.x-intercepts: the point where the graph intersects the x-axis

9.Discriminant: determines how many solutions a quadratic function has and what kind of number they are.

10.When discriminant is negative: 2 complex imaginary solutions

11.When discriminant is zero: 1 real rational solution

12.When discriminant is positive: 2 real solutions