Vertex Form
For y = (x − 4)² + 3, what is the vertex?
Vertex: (4, 3)
Find the x-intercepts:
y = (x − 3)(x + 2)
(3,0) and (-2,0)
Write in standard form:
y = (x + 3)²
y = x² + 6x + 9
Does y = (x − 3)² + 4 have a maximum or minimum?
Minimum
Graph y = (x − 2)². Label the vertex and axis of symmetry.
Vertex: (2, 0)
Axis: x = 2
Opens: Up
For y = (x + 2)² − 5, what are the vertex and axis of symmetry?
Vertex: (−2, −5)
Axis: x = −2
Find the x-intercepts:
y = (x + 4)(x − 6)
(-4,0) and (6,0)
Write in standard form:
y = (x − 4)² + 2
y = x² − 8x + 18
What is the minimum value of y = (x + 2)² − 6?
−6
Graph y = (x + 1)² − 3. Label the vertex and axis of symmetry.
Vertex: (−1, −3)
Axis: x = −1
Opens: Up
For y = −2(x − 3)² + 7, does the parabola open up or down?
Down
For y = (x − 2)(x − 8), what is the axis of symmetry?
x = 5
Write in standard form:
y = −2(x + 1)² + 3
y = −2x² − 4x + 1
What is the maximum value of y = −(x − 4)² + 9?
9
Graph y = (x − 2)(x − 6). Label the x-intercepts, vertex, and axis.
x-intercepts: (2, 0), (6, 0)
Axis: x = 4
Vertex: (4, −4)
Opens: Up
For y = 3(x + 1)² − 4, give the vertex, axis of symmetry, and direction of opening.
Vertex: (−1, −4)
Axis: x = −1
Opens: Up
For y = (x + 3)(x − 7), find the x-intercepts and axis of symmetry.
x-intercepts: (−3,0) and (7,0)
Axis: x = 2
Write in standard form:
y = (x − 5)(x + 2)
y = x² − 3x − 10
Find the maximum or minimum value:
y = 2(x + 5)² − 3
Minimum value: −3
Graph y = (x + 2)(x − 4). Label x-intercepts, axis, vertex, and direction.
x-intercepts: (−2, 0), (4, 0)
Axis: x = 1
Vertex: (1, −9)
Opens: Up
A student says: “The vertex of y = (x − 5)² − 2 is (−5, −2).” Is the student correct? Explain.
No. The vertex is (5, −2). The inside sign is opposite the x-coordinate.
For y = (x − 2)(x − 8), find the vertex.
Axis: x = 5
y = (5−2)(5−8) = −9
Vertex: (5, −9)
Write in standard form:
y = −3(x − 2)(x + 4)
y = −3x² − 6x + 24
A student says: “y = −4(x − 1)² + 6 has a minimum value of 6.” Is the student correct?
No. It opens downward, so it has a maximum. Maximum value: 6.
Quadratic Challenge: y = −2(x − 3)² + 8. Find the vertex, axis, maximum/minimum, and direction.
Vertex: (3, 8)
Axis: x = 3
Maximum: 8
Opens: Down