Graphing Quadratics With VERTEX and Axis of Symmetry

Graphing Quadratics With VERTEX and Axis of Symmetry At the end of the period, you will learn: 1. To compare parabola by the coefficient 2. To find the vertex of a parabola

Warm-up Graph the quadratic equation by factoring. Tell whether the quadratic opens upward or downward 1. y = - 2 x + 7 x + 12 2. f(x)= 2 x + 21 x + 20 3. y = - 2 x - 6 x + 8

Identifying Vertex 2 f(x) = 2 x - x Vertex: (1, 1)

Identifying Vertex 4 Your turn! 2 4 f(x) = x - 4 Vertex: (0, -4)

Comparing Parabola y - axis y Green y = 5 x 2 Purple y = ½x 2 Blue y = ¼ x 2 x x - axis Smaller coefficient = Wider parabola

Graphing with vertex y = ax 2 + bx + c Formula in finding the vertex x = –b_ 2 a y = substitute the value of x 4 0 – Vertex = (__, __) x y

Example Find the vertex of y = -3 x 2 + 6 x + 5 x = –b_ 2 a x = – 6 2(-3) x = – 6 x=1 Formula in finding the vertex x = –b_ 2 a y = substitute the value of x y = -3 x 2 + 6 x + 5 y = -3(1)2 + 6(1) + 5 y = -3 + 6 + 5 y=8 Vertex = (1, 8)

Graph the Parabola y y = -3 x 2 + 6 x + 5 8 6 4 2 Vertex = (1, 8) 1 2 3 4 5 x

Your Turn! Find the vertex of y = x 2 + 2 x – 5 Formula in finding the vertex x = –b_ 2 a y = substitute the value of x x = –b_ 2 a x = – 2 2(1) x = – 2 2 y = substitute the value of x x = – 1 y = – 6 y = x 2 + 2 x – 5 y = (– 1)2 + 2(-1) – 5 y=1 -2– 5 Vertex = (-1, -6)

Graph the Parabola y y = x 2 + 2 x – 5 8 6 4 2 Vertex = (-1, -6) 1 2 3 4 5 x

Graphing Quadratics Review on graphing quadratics At the end of the period, you will master: 1. To graph parabola of this form: y = ax 2 + c

Classwork Sketch the following parabola by finding the vertex 1. y = x 2 + 4 x + 3 4. y = x 2 - 10 x + 20 2. y = –x 2 + 4 x – 4 3. y = x 2 + 3 5. y = - x 2 + 4 x - 4 6. y = –x 2 + 8 x – 5

Warm-up Formula in finding the vertex x = –b_ 2 a y = substitute the value of x Find the VERTEX and graph the PARABOLA 1. y = -3 x 2 + 6 x + 5 Vertex = (1, 8) 3. y = x 2 + 4 x – 5 Vertex = (-2, -9) 2. y = x 2 + 2 x – 5 Vertex = (-1, -6) 4. y = x 2 – 2 Vertex = (0, – 2)

Graphing: y = 2 ax + c 4. y = x 2 – 2 5. y = x 2 + 2 Vertex = (0, – 2) Vertex = (0, 2) y y x x

Graphing: y = 5. y = x 2 2 ax + c 6. y = –x 2 +2 Vertex = (0, 2) y y x x

Classwork Graph the following parabola using: I Finding the solution of the equations (Factoring) 1. y = - x 2 - 9 x + 2. y = x 2 - 6 x + 8 3. y = - x 2 - 7 x + 10 20 II Finding the VERTEX (Using formula) 1. y = x 2 + 4 x + 3 2. y = –x 2 + 4 x – 4 3. y = x 2 + 6 x - 8 III Graphing on y-axis (using vertex) 1. y = x 2 – 1 2. y = –x 2 + 2 3. y = x 2 - 5 4. y = –x 2 + 3