4.1 Notes – Graph Quadratic Functions in Standard Form

Quadratic Function Standard Form Vertex Axis of Symmetry Parabola that is a function in the shape of a U y = ax 2 + bx + c Max or Min of a parabola Line that splits the graph vertically

x – intercepts Set y = 0, factor the equation and solve for x One answerTwo answersNo Real answers

Transformations of a, b, and c. y = ax 2 + bx + cPositive #Negative # a Opens up Has minimum Fraction, wide a > 1, skinny Opens down Has maximum Fraction, wide a < –1, skinny a = 1, normala = –1, normal

b Shift vertex left or right y = ax 2 + bx + c c y – intercept

1. Put the equation in standard from. Determine if the graph opens up or down and if it is normal, skinny, or wide. Standard Form: Opens up wide

1. Put the equation in standard from. Determine if the graph opens up or down and if it is normal, skinny, or wide. Standard Form: Opens down skinny

1. Put the equation in standard from. Determine if the graph opens up or down and if it is normal, skinny, or wide. Standard Form: Opens down normal

2. Identify the vertex. State the max or min. Vertex: ________________ (2, –13) min/max value: _________ y = –13

2. Identify the vertex. State the max or min. Vertex: ________________ (1, 11) min/max value: _________ y = 11

2. Identify the vertex. State the max or min. Vertex: ________________ (0, 5) min/max value: _________ y = 5

3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­- intercepts, and the y-intercepts.

x(x,y) 0 (0,0) (1,1) (2, 4) 1 2 –1 –2 (–1,1) (–2, 4)

Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ (0,0) x = 0 y = 0 0 0

Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ (0,0) x = 0 y = (0,0)(1,1)(2, 4)(–1,1)(–2, 4)

3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­- intercepts, and the y-intercepts.

x(x,y) 0 (0, 9) (1, 8) (2, 5) 1 2 –1 –2 (–1, 8) (–2, 5)

Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ (0, 9) x = 0 y = 9 9 33 x + 3 = 0 x - 3 = 0or x = -3 x = 3

Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ (0, 9) x = 0 y = 9 9 33 (0, 9) (1, 8)(2, 5) (–1, 8)(–2, 5)

3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­- intercepts, and the y-intercepts.

x(x,y) (0, –2) (2, 0) (4, 6) (–2, 0) (–4, 6) –2 –4

Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ (0, –2) x = 0 y = –2 –2  2

Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ (0, –2) x = 0 y = –2 –2  2 (0, –2)(2, 0)(4, 6)(–2, 0)(–4, 6)

3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­- intercepts, and the y-intercepts.

x(x,y) –1 (–1, 3) (0, 0) (1, –9) 0 1 –2 –3 (–2, 0) (–3, –9)

Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ (–1, 3) x = –1 y = 3 0 0, -2 -3x = 0 x + 2 = 0or x = 0 x = -2 -3x -3x(x + 2) = 0

Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ (–1, 3) x = –1 y = 3 0 0, -2 (–1, 3)(0, 0)(1, –9) (–2, 0) (–3, –9)

3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­- intercepts, and the y-intercepts.

x(x,y) (–2, –1) (–1, 0) (0, 3) (–3, 0) (–4, 3) –2 –1 0 –3 –4

Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ (–2, –1) x = -2 y = –1 3 -1, -3 x x 3 1 3x3x+ x (x + 3)(x + 1) = 0 x + 1 = 0x + 3 = 0or x = –3 x = –1

Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ (–2, –1) x = -2 y = –1 3 -1, -3 (–2, –1)(–1, 0)(0, 3)(–3, 0)(–4, 3)

3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­- intercepts, and the y-intercepts.

x(x,y) 1 (1, 0) (2, –2) (3, –8) –1 (0, –2) (–1, –8)

Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ (1, 0) x = 1 y = (x 2 – 2x + 1) = 0 x x -x-x+ -x -2(x – 1) 2 = 0 x – 1 = 0 x = 1 (x – 1) 2 = 0

Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ (1, 0) x = 1 y = (1, 0)(2, –2)(3, –8)(0, –2)(–1, –8)