Quadratic expression values from equations Practice

Warm-upeasy

If $2x^{2} + 8x = 6$ , what is the value of $x^{2} + 4x\textsf{?}$

Divide both sides by $2$ : $x^{2} + 4x = 3$ .

Mid-gameeasy

Suppose $5(x^{2} - 2x) = 15$ . What is the value of $x^{2} - 2x\textsf{?}$

Divide both sides by $5$ : $x^{2} - 2x = 3$ .

Mid-gamemedium

The equation $5x^{2} - 20x + 15 = 0$ is true. What is $x^{2} - 4x\textsf{?}$

Factoring out the GCF $5$ gives $5(x^{2} - 4x + 3) = 0$ . Since $5(0) = 0$ , $x^{2} - 4x + 3 = 0$ . Isolate the desired expression by subtracting $3$ from both sides: $x^{2} - 4x = -3$ .

Mid-gamemedium

Solve for the value of $x^{2} + 3x$ if $3x^{2} + 9x - 12 = 0$ .

Factoring out the GCF $3$ gives $3(x^{2} + 3x - 4) = 0$ . Since $3(0) = 0$ , $x^{2} + 3x - 4 = 0$ . Isolate the desired expression by adding $4$ to both sides: $x^{2} + 3x = 4$ .

Mid-gamemedium

For the equation $6x^{2} - 18x - 24 = 0$ , find the value of $x^{2} - 3x$ .

Factoring out the GCF $6$ gives $6(x^{2} - 3x - 4) = 0$ . Since $6(0) = 0$ , $x^{2} - 3x - 4 = 0$ . Isolate the desired expression by adding $4$ to both sides: $x^{2} - 3x = 4$ .

Mid-gamemedium

If $4x^{2} - 16x + 8 = 0$ , what is $x^{2} - 4x\textsf{?}$

Factoring out the GCF $4$ gives $4(x^{2} - 4x + 2) = 0$ . Since $4(0) = 0$ , $x^{2} - 4x + 2 = 0$ . Isolate the desired expression by subtracting $2$ from both sides: $x^{2} - 4x = -2$ .

Mid-gamemedium

The equation $7x^{2} + 14x - 21 = 0$ holds. What is the value of $x^{2} + 2x\textsf{?}$

Factoring out the GCF $7$ gives $7(x^{2} + 2x - 3) = 0$ . Since $7(0) = 0$ , $x^{2} + 2x - 3 = 0$ . Isolate the desired expression by adding $3$ to both sides: $x^{2} + 2x = 3$ .

Buzzer beatermedium

If $3x^{2} - 12x = 9$ , what is the value of $x^{2} - 4x\textsf{?}$

Divide both sides by $3$ : $x^{2} - 4x = 3$ .

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