Using the Vertex to Write the Quadratic Equation (3.15.2)

Question 1

• Standard form of a quadratic function: f (x) = ax^2+ bx + c.

• Vertex of a parabola: (h, k).
• h = –b/2a.
• k = f (h).

• Vertex form of a quadratic function: f (x) = a(x – h)^2 + k.

Answer 1

• Standard form of a quadratic function: f (x) = ax^2+ bx + c.

• Vertex of a parabola: (h, k).
• h = –b/2a.
• k = f (h).

• Vertex form of a quadratic function: f (x) = a(x – h)^2 + k.

Question 2

• To write a quadratic equation in standard form in vertex form:
• Find the value of h.
• Find the value of k.
• Substitute the values of a, h, and k into vertex form.

Answer 2

• To write a quadratic equation in standard form in vertex form:
• Find the value of h.
• Find the value of k.
• Substitute the values of a, h, and k into vertex form.

Question 3

One way to determine the vertex (h,k) of a parabola is to use
the formulas for h and k shown here.
In this example, a = 1 and b = 4.
So, h = –(4)/2(1) = –2.
k = f (–2) = (–2)2
+ 4(–2) + 1 = –3
The vertex, (h, k), is now known.
Substitute these coordinates to write the equation in vertex
form.
This example points out the value of being accurate and
careful in what you are doing.
You are following the same process:
1. Determine h and k.
(Please use the correct numbers, or …..oops.)
2. Write the vertex.
3. Write the function in vertex form.
You know that this is a down-turned parabola because x
2
has
a negative coefficient.
Find h and k.
When writing the equation in vertex form, be sure to substitute
the a value as well as the h and k values into the vertex form
equation.

Answer 3

One way to determine the vertex (h,k) of a parabola is to use
the formulas for h and k shown here.
In this example, a = 1 and b = 4.
So, h = –(4)/2(1) = –2.
k = f (–2) = (–2)2
+ 4(–2) + 1 = –3
The vertex, (h, k), is now known.
Substitute these coordinates to write the equation in vertex
form.
This example points out the value of being accurate and
careful in what you are doing.
You are following the same process:
1. Determine h and k.
(Please use the correct numbers, or …..oops.)
2. Write the vertex.
3. Write the function in vertex form.
You know that this is a down-turned parabola because x
2
has
a negative coefficient.
Find h and k.
When writing the equation in vertex form, be sure to substitute
the a value as well as the h and k values into the vertex form
equation.