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Quadratic Quest (pp. 1 of 2)
Algebra 2
HS Mathematics
Unit: 05 Lesson: 02
2
Quadratic functions have the general equation y ax
If coordinates for three points on the parabola are known,
then the equation can be found using a 33 system of
equations to find a, b, and c.
For example, the given quadratic function passes through
Q(-1, 1.375), R(2.5, 4) and D(3.5, 2.5). This means…
2
ax + b x + c = y
For Q… a(___) 2 + b(___) + c = ____
For R… a(___) 2 + b(___) + c = ____
For D… a(___) 2 + b(___) + c = ____
bx c
, where a 0 .
This system can be written in matrix form and solved to generate the quadratic function.
Matrices Solution Quadratic Function
a
a
y =
b
b
Check this on a calculator!
c
c
Use this strategy to solve more problems involving quadratic functions.
1) The parabola shown has its vertex at V(0.5, -2.6). A point on
the left side of the parabola is located at L(-3, 2.3).
What are the coordinates for R, the corresponding point
on the right side?
Set up a system to find the constants a, b, and c.
2
ax + b x + c = y
For L… a(___) 2 + b(___) + c = ____
For V… a(___) 2 + b(___) + c = ____
For R… a(___) 2 + b(___) + c = ____
Matrices Solution Quadratic Function
a
a
y =
b
b
Check this on a calculator!
c
c
From the graph, it looks like the function has x-intercepts at approximately -2 and 3. Find these
values, exactly.
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