SME
Grade 11 Math · Problem type
Graph a square root function
Use this for “Graph y = 2√(x + 3) + 1: where it starts, which way it goes, and y at x = 6.”
Chart
Domain (blue bar): [−3, ∞)
Range (orange bar): [1, ∞)
f(6) = 7
The parent y = √x is dashed
This is an example. Type your own values to start a new problem.
y
=
a
−
(
)
+
k
Formulas
y
=
a
×
√
x
−
h
+
k
7 = 2 × √(6 − (−3)) + 1
Assumptions
•
y = a√(x − h) + k starts at (h, k): the parent √x moved right h and up k.
•
The domain is x ≥ h; the range is y ≥ k when a > 0 and y ≤ k when a < 0.
Step-by-step
WE KNOW
a = 2, h = −3, k = 1, x = 6
FIND
output (y)
Step 1 · Find output (y)
Use y = a × √(x − h) + k
Take
the
square
root
of
x
−
h
,
multiply
by
a
,
then
add
k
.
y
=
2
×
√(6
−
(−3))
+
1
y
=
2
×
√
9
+
1
y
=
2
×
3
+
1
y
=
6
+
1
y
=
7
Check
Put the numbers back in. Both sides should match.
7 = 2 × √(6 − (−3)) + 1 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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Related lessons
Radical functions and equations
Main lesson
Extraneous solutions
Use this for “Solve √(x + 7) = x + 1” and reject the extraneous solution.
Graph a cube root function
Use this for “Graph y = 2∛(x + 1) − 3: its center, and y at x = 7” or “Find x where y = 5.”
Rational exponents
Use this for “Evaluate 82/3”, “Graph y = 2x−1/2” or “Solve x3/2 = 27.”