Characteristics of Quadratic Equations
Which of the following statements are true about the horizontal intercepts of a Quadratic Equation in Standard Form? Check all that apply.
There are three possible cases for the number of solutions to a quadratic equation in standard form
If a parabola does not cross the x-axis, then its solutions lie in the complex number system and we say that it has no real x-intercepts
If a parabola touches, but does not cross the x-axis, then its solutions lie in the complex number system and the x-intercept is
(
x
1
,
0
)
\displaystyle {\left({x}_{{1}},{0}\right)}
(
x
1
,
0
)
A QUADRATIC EQUATION in STANDARD FORM is an equation of the form
f
(
x
)
=
a
x
2
+
x
+
c
\displaystyle {f{{\left({x}\right)}}}={a}{x}^{{2}}+{x}+{c}
f
(
x
)
=
a
x
2
+
x
+
c
A QUADRATIC EQUATION in STANDARD FORM is an equation of the form
a
x
2
+
b
x
+
c
=
0
\displaystyle {a}{x}^{{2}}+{b}{x}+{c}={0}
a
x
2
+
b
x
+
c
=
0
If the quadratic equation
a
x
2
+
b
x
+
c
=
0
\displaystyle {a}{x}^{{2}}+{b}{x}+{c}={0}
a
x
2
+
b
x
+
c
=
0
has real number solutions
x
1
\displaystyle {x}_{{1}}
x
1
and
x
2
\displaystyle {x}_{{2}}
x
2
, then the x-intercepts of
f
(
x
)
=
a
x
2
+
b
x
+
c
\displaystyle {f{{\left({x}\right)}}}={a}{x}^{{2}}+{b}{x}+{c}
f
(
x
)
=
a
x
2
+
b
x
+
c
are
(
x
1
,
0
)
\displaystyle {\left({x}_{{1}},{0}\right)}
(
x
1
,
0
)
and
(
x
2
,
0
)
\displaystyle {\left({x}_{{2}},{0}\right)}
(
x
2
,
0
)
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