Graphing Quadratic Equations
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Graphing Quadratic Equations

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Graphing Quadratic Equations Graphing Quadratic Equations Presentation Transcript

  • Graphing Quadratics
    Graphing y = ax2 + bx + c
  • Review
    • We typically see quadratics in the form
    y=ax2+ bx + c
    Where a is the number next to the x2, b is the number next to the x, and c is the constant term
  • Graphing Quadratics
    Graphs of quadratics must include:
    The vertex
    The x-intercepts
    The y-intercept
    y- intercept
    x - intercepts
    Vertex
  • Graphing Quadratics
    Ex) y = 3x2 +6x – 24
    To graph this quadratic we need to find all of the key elements. First let’s start by finding the vertex!
    To find the x-coordinate of the vertex we will use the formula x =
    Plugging in for a and b, we see that x = -6 = -6 = -1 3•2 6
  • Graphing Quadratics
    Ex) y = 3x2 +6x – 24
    Now we will plug in the x-coordinate we found into the equation to find the y-coordinate.
    Y = 3•(-1)2 + 6•(-1) – 24y = 3•(1) + 6•(-1) – 24y = 3 – 6 – 24 y = -27
    So the vertex is at the point (-1, -27)
  • Graphing Quadratics
    Ex) y = 3x2 +6x – 24
    Now we need to find the x-intercepts. To find the x-intercepts you can use one of two ways. The first way is to use the quadratic formula.
    Or we can use the factoring method. In this case, the factoring method is much easier.
  • Graphing Quadratics
    Ex) y = 3x2 +6x – 24
    To factor this equation we see that there is a 3 common to all three terms. So we will first factor that out to the fronty = 3(x2 +2x – 8)
    Now we need factors of -8 that will add to 2.
    y = 3(x + 4)(x – 2)
    Now set each parenthesis to 0 and solve for x.
    x + 4 = 0 and x – 2 = 0 x = -4 and x = 2
  • Graphing Quadratics
    Ex) y = 3x2 +6x – 24
    Finally we need to find the y-intercept. Plug in 0 for x and then solve.
    y = 3x2 +6x – 24y = 3(0)2+6(0) – 24
    y = 0 + 0 – 24
    y = -24
    Now that we have all of the pieces we can put them on the graph.
  • Graphing Quadratics
    Information:
    y = 3x2 +6x – 24
    Vertex (-1, -27)
    x-intercepts x = 4, & x = -2
    y-intercept y = -24
    Graph