Graphing Quadratic Equations

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Graphing Quadratic Equations

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

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