Parabolas Review (Quadratic Functions)

Name Your Forms In what form is the equation y = 3x 2 – 4x + 5 written? – quadratic form

Name Your Forms In what form is the equation y = 3(x – 2) written? – vertex or parabolic form

Name Your Forms In what form is the equation y = x written? – quadratic form – also technically is parabolic or vertex form

Name Your Forms In what form is the equation y = x 2 + 3x written? – quadratic form

Who’s Who in Parabolic Form y = a(x – h) 2 + k up/down movement comes from? k left/right movement comes from? h direction of opening comes from? a

Describe the Functions y = 3(x – 4) opens up, vertex (4, 1), stretch by factor of 3, right 4, up 1 y = -2(x – 3) 2 opens down, vertex (3, 0), stretch by factor of 2, right 3

Describe the Functions y = (x + 2) 2 – 3 opens up, vertex (-2, 3), left 2, down 3 y = 0.5(x + 1) opens up, vertex (-1, 4), shrink by factor of.5, left 1, up 4

Who’s Who in Quadratic Form y = ax 2 + bx + c What does the “a” tell you in quadratic form? direction of opening, stretch or shrink, just like it does in parabolic form

Who’s Who in Quadratic Form y = ax 2 + bx + c What does the “b” tell you in quadratic form? Nothing! This was a trick question. “b” is used, however, in the “x of the vertex” formula

Who’s Who in Quadratic Form y = ax 2 + bx + c What does the “c” tell you in quadratic form? Nothing! Well, that is, unless the question does not have a “bx” term.

Who’s Who in Quadratic Form y = ax 2 + c What does the “c” tell you in THIS version of quadratic form? Since there is no “bx” term, the “c” tells you the y-intercept.

The Vertex Vertex from y = a(x – h) 2 + k? (h, k) Vertex from y = ax 2 + bx + c? Find x by using –b/2a Find y by plugging in x just found

The Vertex Identify the vertices: y = 2(x + 4) 2 – 3? (−4, 3) y = 0.75(x – 1) 2 + 4? (1, 4)

The Vertex Identify the vertex: y = x 2 – 6x + 5? – Find x = −b/2a = −(−6)/2(1) = 3 – Solve for y = (3) 2 – 6(3) + 5 = −4 – Vertex is (3, −4)

The Vertex Identify the vertex: y = 3x x – 4? – Find x = −b/2a = −(12)/2(3) = −2 – Solve for y = 3(−2) (−2) − 4 = – Vertex is (−2, −16)

The Vertex Identify the vertex: y = 4x 2 + 7? – Remember, there is no “bx” term, so x of vertex will be 0. – Since x of vertex is 0, y will be the constant, or 7. – Vertex is (0, 7)