Quadratic functions

1103034703

Level:

Given the graph of the function \( f(x)=2x^2-2x-4 \) and the points \( A \), \( B \), \( C \), \( D \), \( E \), find the solution set of the following equation. \[ 2x^2-2x-4=1 \]

\( \{a;e\} \)

\( \{b;d\} \)

\( \{c;e\} \)

\( \{ c \} \)

1103034702

Level:

Given graphs of the functions \( f(x)=x^2-4x \) and \( g(x)=4x^2-16x+12 \), find the solution set of the following equation. \[ 4x^2-16x+12=x^2-4x \]

\( \{2\} \)

\( \{-4\} \)

\( \{0;4\} \)

\( \{0\} \)

1103034701

Level:

Given graphs of the functions \( f(x)=2x^2-2x-4 \) and \( g(x)=2x+2 \), find the solution set of the following equation. \[ 2x^2-2x-4=2x+2 \]

\( \{-1;3\} \)

\( \{-1;2\} \)

\( \{0;8\} \)

\( \{-4;0\} \)

1103034606

Level:

Given graphs of the functions \( f(x)=x^2-4x\) and \( g(x)=4x^2-16x+12 \), find the solution set of the following inequality. \[ 4x^2-16x+12\leq x^2-4x \]

\( \{2\} \)

\( \mathbb{R} \)

\( \{-4\} \)

\( [1;3] \)

1103034605

Level:

Given graphs of the functions \( f(x)=x^2+2x-3\) and \( g(x)=-x^2+3x-4 \), find the solution set of the following inequality. \[ x^2+2x-3\leq-x^2+3x-4 \]

\( \emptyset \)

\( \mathbb{R} \)

\( (-\infty;0] \)

\( [-3;1] \)

1103034604

Level:

Given graphs of the functions \( f(x)=-2x^2+5x+3\) and \( g(x)=2x+1 \), find the solution set of the following inequality. \[ -2x^2+5x+3 < 2x+1 \]

\( (-\infty;-0.5)\cup(2;\infty) \)

\( (-0.5;2) \)

\( (-\infty;-0.5)\cup(3;\infty) \)

\( (-0.5;3) \)

1103034603

Level:

Given graphs of the functions \( f(x)=x^2-6x+8\) and \( g(x)=-2x+4 \), find the solution set of the following inequality. \[ x^2-6x+8\geq-2x+4 \]

\( \mathbb{R} \)

\( (-\infty;2]\cup[4;\infty) \)

\( \{2\} \)

\( [2;4] \)

1103034602

Level:

Given graphs of the functions \( f(x)=x^2-6x+8\) and \( g(x)=2x+1 \), find the solution set of the following inequality. \[ x^2-6x+8>2x+1 \]

\( (-\infty;1)\cup(7;\infty) \)

\( (1;7) \)

\( (-\infty;2)\cup(4;\infty) \)

\( (1;\infty) \)

1103034601

Level:

Given graphs of the functions \( f(x)=x^2-6x+8\) and \( g(x)=-x^2-2x+24 \), find the solution set of the following inequality. \[ x^2-6x+8\leq-x^2-2x+24 \]

\( [-2;4] \)

\( [2;4] \)

\( [0;24] \)

\( [-6;4] \)

9000033707

Level:

Identify the inequality with a solution graphed in the picture.

\(|x(3 - x)| > 3 - x\)

\(|x(x - 3)| < x - 3\)

\(|3x - x^{2}| > x - 3\)

\(|x^{2} - 3x| < 3 - x\)

\(x^{2} - 3|x| > 3 - x\)

\(x^{2} - 3|x| < x - 3\)

1103034703

1103034702

1103034701

1103034606

1103034605

1103034604

1103034603

1103034602

1103034601

9000033707

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