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Math is Beautiful: QUADRATICS
Transcript of Math is Beautiful: QUADRATICS
4th Period Math is Beautiful: QUADRATICS Vocabulary Descriptions Finding Roots a. in the first half a second at 484 feet
c.6 seconds Answers Axis of Symmetry A vertical line that goes through the vertex. It makes each side a mirror image. It is also the h value of the vertex Discriminant The value under the radical sign in the quadratic function. It tells you how many solutions a function have. Quadratic Formula Tells us what the solutions of a quadratic formula is. Max/Min Point Highest or lowest point on quadratic. Graphing a
Quadratic Function Max/Min Value 1) Direction of opening- this depends on the sign before the variable with the largest exponent. If it is negative the parabola will point downward and vise versa for a positive sign.
2) Axis of Symmetry- the axis of symmetry goes through the vertex of a quadratic
3) Vertex- the highest or lowest point on a graph
4) Y-intercept- where the quadratic hits the y-axis
5) Table- a useful source to see your x and y values
6) Min/ Max value- the highest or lowest y value on a qudratic parabola Discriminant The discriminant is the value underneath the radical in the quadratic equation. If it has a value greater than zero, then the parabola hits the x-axis two times. If the discriminant is equal to zero, than it has only one solution. If it is less than zero, the parabola will have an imaginary solution set. Writing a Quadratic
Equation 1) Find two roots for example purposes. For this example, allow the roots to be 4 and -6.
2) Put the roots into the form y = (x - a) (x - b), where one root is a and the other for b. In this example, 4 and -6 turn into y = (x - 4) (x + 6).
3) Multiply the two expressions with x together. First, multiply the terms in the second parentheses with the x of the first expression. The do the same with the constant in the first parentheses. In this example, multiplying x to x + 6 becomes x² + 6x, and -4 to x + 6 becomes -4x - 24. The equation is now
y = x² + 6x - 4x - 24.
4) Combine like terms to finalize the equation. Concluding this example, 6x and -4x are similar terms, so combining them results in 6x - 4x = 2x. So the quadratic equation reads y = x² + 2x - 24.
This is standard form. To turn this into vertex form you can add 24 to both sides wich will look like y+24= x² + 2x then factor out the highest exponent wich will look like y+24= (x+2)². Finally you move the 24 back to its original position and you will end up with y= (x+2)²-24. This is known as vertex form. Word Problem Chris Brown went cliff diving with some friends. The speed as a function of the time from him jumping could be modeled by the function: h(t)=-16t^2+16t+480, where t is the time in seconds and h is his height in feet.
a. How long did it take for Chris to reach his maximum height?
b. What was the highest point that Jason reached?
c. When did Chris hit the water? Cliff Diving With Chris and Friends Standard Form of Quadratic Formula Quadratic equation is an equation of the form ax^2 +bx+c=0 , where a≠0 .
The form ax^2+bx+c=0 is called the standard form of the quadratic equation.
In standard form: 2x 2 −x−4=0 Vertex Quadratic's turning point.
The point where a line can cut the parabola into two.
Highest/lowest point. Vertex form Is a Simplified form of standard.
Where (h,k) is the vertex.
In the parentheses, the sign is opposite. (+ = left and - = right) Zeros/Roots/Intercepts It is a solution to the polynomial equation, P(x) = 0.
It is that value of x that makes the polynomial equal to 0. Arithmetic Series REMEMBER MATH IS B-E-A-UTIFUL!! FIN! Transformations The y-value of the vertex A series which has a constant difference between terms. 5, 7, 9, 11, 13, …