What's Going On? Quiz Tomorrow What's My Vertex? Find my Vertex! What's my y Intercept? Learning Goal I will understand how to find the zeros or x intercepts of a quadratic equation. 1
What's my Vertex? y = (x - 4)(x - 6) x-value of vertex y-value of vertex 2
What's my Vertex? y = (x - 1)(x - 5) x-value of vertex y-value of vertex 3
What's my Vertex? y = -(x + 2)(x + 6) x-value of vertex y-value of vertex 4
What's my Vertex? y = -(x - 5)(x - 9) x-value of vertex y-value of vertex ` 5
Finding the Vertex of a Parabola given a Factored Form Equation Step 1: Determine the zeros. Step 2: Determine the x value of the vertex by finding the average of the zeros. Step 3: Determine the y value of the vertex by substituting the x value into the original equation and solving for y. 6
What's my Vertex? y = (x + 2)(x - 4) x-value of vertex y-value of vertex 7
What's my Vertex? y = (x + 6)(x - 2) x-value of vertex y-value of vertex 8
What's my Vertex? y = -2(x + 1)(x - 3) x-value of vertex y-value of vertex 9
Find my Vertex! y = -2(x + 1)(x - 3) To find the x-value of the vertex of a parabola given in factored form we need to go HALF WAY between the two zeros! We already knew that these parabolas were "symmetrical". The vertical line of symmetry is called the axis of symmetry 10
y = -2(x + 1)(x - 3) x-value of the Vertex Find my Vertex! The zeros are x = 1, +3 To find the axis of symmetry, add up the zeros and divide by two! axis of symmetry = ( 1) + (+3) 2 = +2 2 = 1 11
Find my Vertex! y = -2(x + 1)(x - 3) So the axis of symmetry is x = 1 This means that the x value of the vertex is 1! y-value of the Vertex How can we now find the y value of the vertex? 12
Find my Vertex! y = -2(x + 1)(x - 3) y-value of the Vertex If we know the x value of the vertex, we can find the y value of the vertex by just plugging the x value into our equation and solving for y! This will us that when x is 1 (at the vertex) y is... 13
Find my Vertex! y = -3(x - 3)(x + 9) 14
Find my Vertex! y = 5x(x + 2) 15
Find my Vertex! Determine the vertex of each parabola. y = (x + 4)(x + 12) y = 8(x - 5)(x + 9) y = (x - 7)(x - 1) y = 2(x - 2)(x - 4) y = -3(x + 2)(x + 8) y = -0.5(x - 1)(x + 7) y = 6x(x - 2) y = -3x(x - 8) 16
What's my y Intercept? If you were given the factored form equation y = (x 4)(x + 3) and asked to find the y intercept, what would you do? Remember: the y-intercept is the c-value in a standard form equation (ax 2 + bx + c) 17
What's my y Intercept? y = (x 4)(x + 3) You could expand (or FOIL) this into standard form and find it that way! 18
What's my y Intercept? y = (x 4)(x + 3) So the y-intercept is -12... Is there a quicker way? 19
What's my y Intercept? y = (x + 5)(x 2) 20
What's my y Intercept? y = (x + 6)(x + 1) 21
What's my y Intercept? y = (x 10)(x 3) 22
What's my y Intercept? y = 2(x + 4)(x 5) 23
What's my y Intercept? y = 2(x + 4)(x 5) The y-intercept is -40 NOT -20!! 24
What's my y Intercept? y = a(x r)(x s) To find the y-intercept of a parabola in factored form: Multiply the a-value by r and s. Be sure to keep the signs as you see them! 25
What's my y Intercept? y = 6x(x 3) y Intercept = CAREFUL! When we only have one set of brackets, one of the zeros is actually zero! So be sure to multiply by 0! 26
What's my y Intercept? y = 6x(x 3) If you think about this one, it actually makes sense! We know that this parabola has an x intercept at 0 and at +3. If x = 0 when y = 0, this parabola must have its y intercept at 0! A y intercept is the point where the curve crosses the y axis (where x = 0)! 27
What's my y Intercept? Determine the vertex and y intercept of each parabola. y = (x + 4)(x + 12) y = 8(x - 5)(x + 9) y = (x - 7)(x - 1) y = 2(x - 2)(x - 4) y = -3(x + 2)(x + 8) y = -0.5(x - 1)(x + 7) y = 6x(x - 2) y = -3x(x - 8) 28