2010012205
Level:
C
Find all the values of the real parameter \( p \) such that \( f(x)=-2(x+3)^2+p \) is nonpositive for all \( x\in\mathbb{R} \).
\( p\in(-\infty;0] \)
\( p\in [ 0;\infty) \)
\( p\in(-\infty;-3] \)
\( p\in [ -3;\infty) \)
Quadratic functions
9000007101
Level:
C
Consider a family \(M\)
of quadratic functions, as shown in the picture. Any quadratic function in this family
is given by the analytic expression
\[
y = ax^{2} + bx + c
\]
where \(a\),
\(b\) and
\(c\) are real constants and
\(a\not = 0\). For each function
the set \(K\) denotes the
set of \(x\)-intercepts. Complete the statement. „The analytic expressions for functions in the family
\(M\) differ
only in ....”
the coefficient \(a\)
the coefficient \(b\)
the coefficient \(c\)
the set \(K\)
9000007102
Level:
C
Consider a family \(M\)
of quadratic functions, as shown in the picture. Any quadratic function in this family
is given by the analytic expression
\[
y = ax^{2} + bx + c
\]
where \(a\),
\(b\) and
\(c\) are real constants and
\(a\not = 0\). For each function
the set \(K\) denotes the
set of \(x\)-intercepts. Complete the statement. „The analytic expressions for functions in the family
\(M\) differ
only in ....”
the coefficient \(c\)
the coefficient \(a\)
the coefficient \(b\)
the solution set \(K\)
9000007103
Level:
C
Consider a family \(M\)
of quadratic functions, as shown in the picture. Any quadratic function in this family
is given by the analytic expression
\[
y = ax^{2} + bx + c
\]
where \(a\),
\(b\) and
\(c\) are real constants and
\(a\not = 0\). For each function
the set \(K\) denotes the
set of \(x\)-intercepts. Complete the statement. „The analytic expressions for functions in the family
\(M\) share
only ....”
the value of the coefficient \(a\)
the value of the coefficient \(b\)
the value of the coefficient \(c\)
the solution set \(K\)
9000007104
Level:
C
Consider a family \(M\)
of quadratic functions, as shown in the picture. Any quadratic function in this family
is given by the analytic expression
\[
y = ax^{2} + bx + c
\]
where \(a\),
\(b\) and
\(c\) are real constants and
\(a\not = 0\). For each function
the set \(K\) denotes the
set of \(x\)-intercepts. Complete the statement. „The analytic expressions for functions in the family
\(M\) share
only ....”
the value of the coefficient \(b\)
the value of the coefficient \(a\)
the value of the coefficient \(c\)
the solution set \(K\)
9000007105
Level:
C
Consider a family \(M\)
of quadratic functions, as shown in the picture. Any quadratic function in this family
is given by the analytic expression
\[
y = ax^{2} + bx + c
\]
where \(a\),
\(b\) and
\(c\) are real constants and
\(a\not = 0\). For each function
the set \(K\) denotes the
set of \(x\)-intercepts. Complete the statement. „The analytic expressions for functions in the family
\(M\) share
only ....”
the solution set \(K\)
the value of the coefficient \(a\)
the value of the coefficient \(b\)
the value of the coefficient \(c\)
9000033707
Level:
C
Identify the inequality with a solution graphed in the picture.
\(|x(3 - x)| > 3 - x\)
\(|x(x - 3)| < x - 3\)
\(|3x - x^{2}| > x - 3\)
\(|x^{2} - 3x| < 3 - x\)
\(x^{2} - 3|x| > 3 - x\)
\(x^{2} - 3|x| < x - 3\)