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## Quadratic Functions

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**Chapter 2 Section 1**Quadratic Functions By: Brooke Tellinghuisen Kelli Peters Austin Steinkamp**Vocabulary**Term 2x-2 Polynomials Degree Leadingcoefficient**Definition Of Polynomial function**• Example of Polynomial Functions • Polynomials are classified by degree. • Formula of Polynomial Function**Definition of Quadratic function**2nd degree polynomials functions are called quadratic functions. Example of Quadratic Functions Formula of Quadratic Function NOTE: a, b, and c are real numbers with a 0.**Quadratic Formula**Used to find zeros (roots) in a quadratic function.**Quadratics**General form y=ax2+bx+ c Vertex Form y= a(x-h)2+k Factored form y=(x-r1)(x-r2) Vertex Vertex (h,k) Vertex: standard form or vertex form Roots: Standard Form or factored form Roots: Quadratic formula or factored form Roots: x= r1,r2**The graph for a quadratic function is a “U”-shaped**graph, called a parabola. If the leading coefficient is positive, the graph opens upward. If the leading coefficient is negative, the graph opens downward.**The point where the axis intersects the parabola is the**vertex. If a > 0, the vertex is the point with the minimum y-value on the graph. If a < 0, the vertex is the point with the maximum y-value on the graph.**Practice Problem**• F(x)=(x-2)^2 • Tell what direction the graph moves and if it opens up or down.**Practice problem answer**Since the 2 is connected with the x in the parentheses the graph moves the opposite way of what u think it would. Since it’s a subtraction problem it moved to the right.**Practice Problem 2**• Find the vertex and x-intercepts of the equation f(x)=x2-5**Answer to practice problem 2**• Take (x2-5) and set equal to zero • x2-5=0 To find your vertex +5 =+5 x2 =5 Use the formula to find your vertex Plug 0 back into the equation and solve. Those would be your x-intercepts Your answer is (0, -5)**AreaExample**• Area Problem A(x)=width x length A farmer has 200 yards of fencing. Write the area as a function of x, if the farmer encloses a rectangular area letting the width equal to x. What is my maximum area? What are my zeros? Do the zeros match common sense? L X-100=x(-x) -x2+100x Finding the Vertex -100/ 2(-1) (50,2500) 2x+2L=200 -2x -2x 2L=200-2x 2L/2=200-2x/2 L=100-x X X L**Projectile Motion Function**• A function of height that depends on time. a = acceleration of gravity. b = initial velocity in which object is thrown. c = initial height.**Projectile motion problem**• An object is launched at 19.6 meters per second from a 58.8 meter tall platform. • The equation for the objects highest s at time t seconds after launch is s(t)=-4.9t2+19.6t+58.8, where s is in meters. • When does the object strike the ground?**Answer to Projectile motion problem**• 0=-4.9t2+19.6t+58.8 • 0=t2-4t-12 • 0=(t-6)(t+2) • So T=6 and -2. The answer cant be negative so the object hit the ground at 6 seconds after the launch.