2 Quadratic functionA QUADRATIC FUNCTION is a function that can be written in the standard form: f(x) = ax2 + bx + c where a≠ 0
3 Graphing quadraticThe graph of a quadratic function is U-shaped and it is called a PARABOLA. a < 0 a > 0
4 Parts of a Parabola!!! Vertex: highest or lowest point on the graph. 2 ways to find Vertex:1) Calculator:2nd CALCMIN or MAX2) Algebraically
5 Parts of a Parabola!!!Axis of symmetry: vertical line that cuts the parabola in half Always x = a Where a is the x from the vertex
6 Parts of a Parabola!!!Corresponding Points: Two points that are mirror images of each other over the axis of symmetry.
7 Parts of a Parabola!!!Y-intercept: Where the parabola crosses the Y-Axis. To find: Look at the table where x is zero.
8 Parts of a Parabola!!!X- Intercept: The the parabola cross the x-axis. To find: 2nd CALC Zero, Left Bound, Right Bound FIND EACH ONE ON ITS OWN!!
9 Try Some!Find the vertex and axis of symmetry for each parabola.
10 Try Some!Find the Vertex, Axis of Symmetry, X-Int and Y-int for each quadratic equation.y = x2 + 2xy = -x2 + 6x + 5y = ¼ (x + 5)2 – 3
11 Try Some!Identify the vertex of the graphs below, the axis of symmetry and the points that correspond with points P and Q.
12 Writing Quadratic equations We can use systems of equations to write quadratic equations.A = 3 b= -5 and c = 1
13 The calculator can do it for you! Find a quadratic equation to model the level of water in the water tank. How much water is in the tank after 35 second? When is it empty? STAT ENTER X-values in L1 and y-values in L2 STAT CALC 5: QuadReg ENTER
29 Word ProblemsA ball is thrown in the air. The path of the ball is represented by the equation h = -t2 + 8t. What does the vertex represent? What does the x-intercept represent?
30 Word ProblemsA lighting fixture manufacturer has daily production costs of C = .25n2 – 10n + 800, where C is the total daily cost in dollars and n is the number of light fixture produced. How many fixtures should be produced to yield minimum cost.
42 Factoring a trinomial: 1. Write two sets of parentheses, ( )( ). These will be the factors of the trinomial.2. Product of first terms of both binomials must equal first term of the trinomialNext
43 Factoring a trinomial: 3. The product of last terms of both binomials must equal last term of the trinomial (c).4. Think of the FOIL method of multiplying binomials, the sum of the Outer and the Inner products must equal the middle term (bx).
44 Slide Factor Divide Reduce More Factoring! When a does NOT equal 1. StepsSlideFactorDivideReduce