Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

- Linear-Non Linear Functions edmodo by shumwayc 728 views
- Non linear function by venyclaudia 1637 views
- Mathematics Graph of Non Linear fun... by Rohan Byanjankar 347 views
- Linear non linear by VARANASI RAMA RAO 9823 views
- M8 lesson 3 2 linear & non-line... by lothomas 240 views
- Linear programming - Model formula... by Joseph Konnully 83569 views

No Downloads

Total views

845

On SlideShare

0

From Embeds

0

Number of Embeds

5

Shares

0

Downloads

44

Comments

0

Likes

1

No embeds

No notes for slide

- 1. Quadratic Functions <ul><li>By Chris Dudley and Jose Ortega </li></ul>
- 2. What is a Quadratic Function? <ul><li>A quadratic function is any equation with a degree* of two. </li></ul><ul><li>In standard form a quadratic equation is ax²+bx+c. </li></ul><ul><li>A quadratic equation is a trinomial** expression because in standard form it adds three terms (ax², bx, and c). </li></ul>
- 3. Quadratic Explosion Letter Part a Quadratic coefficient*** (what your are multiplying the value of x² by). x Indeterminate**** value (the value that changes along the x value of the graph). b The linear coefficient (what you are multiplying x by and adding to ax²). c The constant coefficient (what you are adding to the total value of ax²+bx).
- 4. A Quadratic Graph <ul><li>When you graph a quadratic equation the line forms a symmetrical U-shape called a parabola (puh-rab-uh-luh). </li></ul><ul><li>Altering the A value causes the parabola ’ s curvature to change. </li></ul><ul><li>Altering the C value changes the height of the vertex. </li></ul><ul><li>Altering the B value changes the site of the vertex. </li></ul>
- 5. Parts of a Graph <ul><li>The vertex is at the center point of the parabola where there is no other point on the parabola with the same Y-value. </li></ul><ul><li>The Y-intercept is the point where the line crosses the Y-axis at x=0 </li></ul><ul><li>The X-intercept is where the line intercepts the x-axis at Y=0. A parabola can have 1, 2, or no X-intercpets. If the vertex falls on the x-axis there is one X-intercept. If the vertex falls under the x-axis there are two X-intercepts. If the vertex is over the x-axis there are no X-intercepts (Note: these rules apply if the A-value is positive, if it is negative then vice-versa applies.) </li></ul>
- 6. The A Value and Graphing <ul><li>The A value or quadratic coefficient is the value by which you multiply the solution of x² (remember order of operations, don ’ t multiply x by a and then square it). </li></ul><ul><li>The quadratic coefficient can never equal zero. If it were zero, it would make the product of ax² zero and leave only a linear expression (bx+c). </li></ul>
- 7. The A Value and Curvature <ul><li>If the quadratic coefficient is over one then it makes the standard parabola (x²) steeper. This happens because it makes the solution of x² larger with multiplication. </li></ul><ul><li>If the quadratic coefficient is under one, then it makes the standard parabola less steep. This happens because whenever a fraction or decimal is multiplied it makes, that fraction of the solution to x². </li></ul>2x² .5x²
- 8. Negative A Values <ul><li>A negative A value takes the standard parabola (x²) and flips it upside down. </li></ul><ul><li>This happens because any time a number is multiplied or squared by itself the rules of integers cause the value to be positive. However, when that positive value of x² is multiplied by a negative, the solution turns negative. </li></ul><ul><li>Negative A values can also change the curvature as well as flip a parabola. In this case values over -1 (these values do appear larger however because we ’ re in the negatives) but below zero cause the steepness to decrease. Values below -1 cause the steepness to increase. </li></ul>(-1)x²
- 9. The B Value <ul><li>The B value or linear coefficient is the value that you multiply x by in the linear term (bx). You then add the value onto the value of ax². </li></ul><ul><li>Although it is hard to tell the exact way the linear coefficient will shape the graph, it is easy to find out the approximate shape of the graph will. </li></ul><ul><li>Unless there is a C-value, one of the x-intercepts will be zero. </li></ul>
- 10. B Value Graphs <ul><li>A linear coefficient does not change the curvature of the parabola. It instead moves the whole parabola to the side and down some. </li></ul><ul><li>The quadratic coefficient will always move the vertex into the opposite integer on the x axis. </li></ul><ul><li>The reason why a parabola moves to a side and then down is because in the opposite integer of the linear coefficient the value will be negative. This causes a depression in the parabola until ax^2 can create a larger value. </li></ul><ul><li>With a negative value the b value moves the vertex into its own integer along the x-axis and then moves it up. </li></ul>Draw Graphs here:
- 11. The C Value <ul><li>The c value or constant coefficient is what you finally add to the value of ax²+bx+c. </li></ul><ul><li>The constant coefficient only moves the vertex of the graph and all its points up and down. </li></ul><ul><li>Interesting fact: The C value can never subtract the absolute value***** of ax²+bx (-|ax²+bx|) because it would always end up creating a zero. </li></ul>
- 12. The C Value Graph <ul><li>Adding a negative c value always moves a parabola down. Adding a positive always moves the parabola up. </li></ul><ul><li>The effects of the constant coefficient is not affected by any other values in the standard form. </li></ul>x²+(-1) Or x²-1 x²+1
- 13. FAQs (Frequently Asked Questions) <ul><li>What ’ s the difference between a quadratic equation and an exponential one?: In an exponential equation the exponent changes. In a quadratic equation the growth factor****** changes. </li></ul><ul><li>What about equations with a degree of three?: Equations with a degree of three are completely different. They do not graph a parabola and do not have the same standard form. </li></ul><ul><li>What is the purpose of quadratic equations?: As we are learning, quadratic equations are often used in connection with the measurement of area of rectangles. Cubics are used to find the volume of a cube. </li></ul>
- 14. Vocabulary <ul><li>*Degree: The highest power of any term of a polynomial (Algebra to Go). </li></ul><ul><li>**Trinomial: A polynomial (the sum of terms) with three terms (the product of constants and variables) (Algebra to Go). </li></ul><ul><li>***Coefficient: A numerical value in a term of an agebraic expression (Algebra to Go). </li></ul><ul><li>****Indeterminate: (Of an equation) able to be satisfied by more than one value (Dictionary.com) </li></ul><ul><li>*****Absolute Value (indicated with | |): The distance from zero on a number line. Absolute value is never negative (Algebra to Go). </li></ul><ul><li>******Growth Factor: The number that is multiplying by itself the amount of times the exponent states(my own definition). </li></ul>
- 15. Sources <ul><li>Algebra to Go </li></ul><ul><li>Dictionary.com </li></ul><ul><li>Wolframalpha.com </li></ul><ul><li>Coolmath.com </li></ul><ul><li>Graphs from freemathhelp.com </li></ul><ul><li>Picture on slide one from Wikipedia.org </li></ul>

No public clipboards found for this slide

×
### Save the most important slides with Clipping

Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.

Be the first to comment