Lesson 4-2b Notes: Standard Form Of Quadratic Function Worksheet
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3LESSON 4-2B NOTES: STANDARD FORM OF QUADRATIC FUNCTION
2
STANDARD FORM: f(x) = ax
+ bx + c, where a
0;
2
VERTEX FORM:
f(x) = a(x
h)
+ k, where a
0 and the vertex is (h, k)
* Vertex: The x-coordinate of the vertex is x =
* The y-coordinate of the vertex is the y-value of the function for x =
, or f(
)
(
)
, f(
Vertex =
* The y-intercept is (0, c)
24x + 50?
2
EXAMPLE 1: What is the vertex form of y = 3x
2
y = ax
+ bx + c
24x + 50
2
y = 3x
Verify that the equation is in standard form.
b = 24, a = 3
Find b and a.
b
x -coordinate =
For an equation in standard form, the x-coordinate of the
2
a
b
vertex can be found by using
.
x
2
a
24
Substitute.
2(3)
= 4
Simplify.
24(4) + 50 Substitute 4 into the standard form to find the y-coordinate.
2
y-coordinate = 3(4)
= 2
Simplify.
y = 3(x 4)
2
+ 2
Substitute 4 for h and 2 for k into the vertex form.
Once the conversion to vertex form is complete, check by multiplying.
8x + 16) + 2
2
y = 3(x
24x + 50
2
y = 3x
24x + 50
2
The result is the standard form of the equation: y = 3x
2
EXAMPLE 2: What is the vertex form of y = 2x
12x + 11
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