MBF3C – Quadratics II
Date: _________________________
x-Intercepts of a Quadratic Relation
The __________________ of a quadratic equation are also called the __________ of the parabola
x-intercepts (zeros)
roots
To graph a parabola in VERTEX form,
(
)
k
h
x
a
y
+
−
=
2
,
the following is needed:
coordinates of the vertex
(h, k)
equation of the axis of symmetry
x = h
y –
intercept
x = 0 at the y-intercept
y –
intercept mirror point
Same distance from the axis of symmetry as y-intercept
Direction of opening
+a
Æ
opens up,
– a
Æ
opens down
Vertically stretched
|a| > 1
Æ
step pattern 1a, 3a, 5a, etc.
Vertically compressed
|a|< 1
Æ
a fraction/decimal < 1
To graph a parabola in STANDARD form,
,
the following is needed:
c
bx
ax
y
+
+
=
2
coordinates of the roots
(given by the factors)
i.e. y
=
(x – 5)(x – 13)
roots:
x
=
5 and x
=
13
axis of symmetry
(x value of vertex)
add the roots and divide by 2
x
=
5 + 13
x
=
9 (the midpoint between the roots)
2
the optimal value
(y value of vertex)
Sub x
=
9 into the Standard form of the equation.

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- Fall '14
- nunu
- Quadratic equation, optimal value