1. Vertex and Intercept Form of Quadratic Function
Standard: MM2A3c Students will
Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of
symmetry, zeros, intercepts,
extrema, intervals of
increase, and decrease,
and rates of change.

2. Vertex Form of the Quadratic
Determine the vertex of the following functions:
f(x) = 2(x – 1)2 + 1
g(x) = -(x + 3)2 + 5
h(x) = 3(x – 2)2 – 7

3. Vertex & Axis of Symmetry Summary
Put equation in standard form f(x) = ax2 + bx + c
Determine the value “a” and “b”
Determine if the graph opens up (a > 0) or down (a < 0)
Find the axis of symmetry:
Find the vertex by substituting the “x” into the function and solving for “y”
Determine two more points on the same side of the axis of symmetry
Graph the axis of symmetry, vertex, & points

4. Vertex Form of the Quadratic
Determine the vertex of the following equations:
f(x) = 2(x – 1)2 + 1
g(x) = -(x + 3)2 + 5
h(x) = 3(x – 2)2 – 7
Compare the equations and the vertices. Do you notice a pattern?
V = (1, 1)
V = (-3, 5)
V = (2, -7)
The x part is the opposite sign of the number inside the brackets and the y part is the same as the number added or subtracted at the end.

5. Vertex Form of the Quadratic
The vertex form of the quadratic equation is of the form:
y = a(x – h)2 + k, where:
The vertex is located at (h, k)
The axis of symmetry is x = h
The “a” is the same as in the standard form
The “a” is the stretch of the function
The vertex is shifted right by h
The vertex is shifted up by k

6. Vertex Form of the Quadratic
From y = x2
Stretch factor Vertex Shift VERTICAL amount
y = a(x – h)2 + k
Vertex Shift HORIZONTAL amount

8. In Class: Do page 63 of Note Taking Guide
Do first 6 problems of Henley Task Day 2 – be sure to graph the y = x2 for each graph.

9. In Class Do page 64 of the Note Taking Guide
Do Day 2 of the Henley Task, # 4a – 4e all

10. Intercept Form of the Quadratic Function
How can we determine the vertex of the following equations without putting them in standard form?
f(x) = (x – 3)(x – 1)
g(x) = 2(x + 1)(x + 4)
h(x) = -3(x – 2)(x + 3)
Determine the x-intercepts (zero prod rule)
Find the axis of symmetry (average)
Find “y” value of the vertex (sub into f(x))
V = (2, -1)
V = (-2.5, -4.5)
V = (-0.5, 18.75)

11. Homework
Page 65, # 1, 2, and 19 – 22 all

12. Convert from Standard to Vertex Form
Standard: MM2A3a Students will
Convert between standard and vertex form.

13. Convert from Standard to Vertex Forms
We converted from Vertex form to Standard form of the quadratic function above in slide 3 by expanding the
(a – h)2 term and combining like terms
How can we convert from Standard form to Vertex form?

14. Convert from Standard to Vertex Forms
Look at the standard form:
y = ax2 + bx + c, where a ≠ 0
And look at the Vertex form:
y = a(x – h)2 + k
“h” is the axis of symmetry, which is the “x” part of the coordinates of the vertex
“k” is the “y” part of the vertex

15. Convert from Standard to Vertex Forms
How did we find the axis of symmetry?
This is the “h” of the vertex form
How did we then find the “y” part of the vertex?
Substitute the x into the original equation and solve for y.
This is the “k” of the vertex form
The “a” is the same for both forms

16. Convert from Standard to Vertex Forms
Convert the following functions to vertex form:
f(x) = x2 + 10x – 20
y = (x + 5)2 - 45
g(x) = -3x2 – 3x + 10
y = -3(x + 0.5)
h(x) = 0.5x2 – 4x – 3
y = 0.5(x – 4)2 - 11