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Algebra Examples
Popular Problems Algebra Find the Domain and Range y=3/2x^2+4x-9
y
=
3
2
x
2
+
4
x
−
9
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
(
−
∞
,
∞
)
Set-Builder Notation:
{
x
|
x
∈
R
}
The range is the set of all valid
y
values. Use the graph to find the range.
Interval Notation:
[
−
35
3
,
∞
)
Set-Builder Notation:
{
y
∣
∣
∣
y
≥
−
35
3
}
Determine the domain and range.
Domain:
(
−
∞
,
∞
)
,
{
x
|
x
∈
R
}
Range:
[
−
35
3
,
∞
)
,
{
y
∣
∣
∣
y
≥
−
35
3
}
image of graph
Answer:
y ≤ 66.28 -> -∞
Step-by-step explanation:
y = a (x-h)² + k ... (h,k): vertex
y = - 32x² + 90x + 3
= -32 (x² - (90/32)x + (90/64)²) + (3 + (32)*(90/64)²)
= -32 (x² - 2*(90/64)x + (90/64)²) + (3+63.28) ... 90/64=1.41
= -32 (x - 1.41)² + 66.28
h = 1.41
k = 66.28 .... extremum of y value
y ≤ 66.28 (y is real number)
