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WARM UP

WARM UP. Find the characteristics of the following parabola Domain Range X-intercept Y-intercept Interval of increase. Types of Quadratic Equations. Vertex form, Standar form, Intercept form. Vertex Form. In the form of y=a(x-h) ² + k Advantages

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WARM UP

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  1. WARM UP • Find the characteristics of the following parabola Domain Range X-intercept Y-intercept Interval of increase

  2. Types of Quadratic Equations Vertex form, Standar form, Intercept form

  3. Vertex Form • In the form of y=a(x-h)² + k • Advantages • Can easily determine vertex of a parabola and if it opens up or down • Disadvantages • Cannot determine zeros or y intercept from equation The x value of your vertex with the sign changed The y value of your vertex

  4. Standard form • In the form of y= ax² +bx +c • Advantages • Can easily tell if parabola opens up or down and the y intercept (0,c) • Disadvantages • Need to use x = -b/2a to determine vertex • Difficult to determine zeros

  5. Introducing – Intercept form • Y= a(x-p)(x-q) If you set each bracket to 0, you can find your x-intercept. Opens up or down Used to calculate your zeros

  6. Intercept form Example • Y = 2(x-6)(x+2) • Opens up or down? • Up  because the 2 is positive • Find zeros by setting each bracket to zero X-6=0 x+2 = 0 X=6 x = -2 (6,0) and (-2,0) are your x intercepts

  7. Name that form • Y = 2x² + 4x + 6 • STANDARD • Y = 3(x-3)(x+4) • INTERCEPT • Y = 5(x-4)² - 5 • VERTEX

  8. Practice • Y = 4x² + 16x – 4 • Y intercept? • (0, -4) • Vertex? = -2 Then plug back into equation Y = 4(-2)² + 16(-2) -4 Vertex (-2, -20)

  9. Practice Y = 2(x-3)² + 5 Vertex? (3, 5) Opens up or down? Up

  10. Practice Y = 4(x-4)(x-2) X-intercepts? x = 4 x = 2 Standard form of the equation? 4x² - 24x + 32

  11. How do you find the vertex when in intercept form? • Take the original equation • Y = 4(x-4)(x-2) • Put it into standard form • 4x² - 24x + 32 a. 4 b. -24 c. 32 • Find the vertex using • X= x=3 • Y = 4(3)² -24(3) + 32 • VERTEX ( 3, -4)

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