Solving Systems of Linear-Quadratic Equations

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What is a system of linear-quadratic equations?

Back

A system of linear-quadratic equations consists of at least one linear equation and one quadratic equation that are solved simultaneously.

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What is the substitution method in solving equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you determine the number of solutions in a linear-quadratic system?

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The number of solutions can be determined by analyzing the graphs of the equations; they can intersect at zero, one, or two points.

Front

What does it mean if a system of equations has two solutions?

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It means that the graphs of the equations intersect at two distinct points.

Front

What is the general form of a quadratic equation?

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The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

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What is the vertex of a quadratic function?

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The vertex is the highest or lowest point of the parabola represented by the quadratic function.

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How can you find the vertex of a quadratic function in standard form?

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The vertex can be found using the formula (-b/2a, f(-b/2a)) where f(x) is the quadratic function.

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What is the significance of the discriminant in a quadratic equation?

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The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

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What is the graphical representation of a linear equation?

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A linear equation is represented graphically as a straight line on a coordinate plane.

Front

What is the standard form of a linear equation?

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The standard form of a linear equation is Ax + By = C, where A, B, and C are constants.