Quadratics Standard Form
By: Vikash Singh
Standard Form Equation:
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.
- 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.
Completing The Squares:
- Transforms a standard equation into vertex form to get the vertex and the maximum/minimum value.
- 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)
Here Is a Video to Help You Understand Further How to Complete the Square:
Standard Form Example:
Here is an Example of Completing The Square:
- 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:
- 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.
- 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,
- 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.
- 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.
- 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.
- 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:
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