Linear / Quadratic Systems of Equations

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What is a linear equation?

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What is a quadratic equation?

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How do you find the vertex of a quadratic function?

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What does it mean for a system of equations to be consistent?

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A system of equations is consistent if it has at least one solution. This can be either one unique solution or infinitely many solutions.

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What does it mean for a system of equations to be inconsistent?

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A system of equations is inconsistent if it has no solutions, meaning the lines represented by the equations do not intersect.

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What is the method of substitution in solving systems of equations?

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

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What is the method of elimination in solving systems of equations?

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The method of elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

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How do you graph a quadratic function?

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To graph a quadratic function, identify the vertex, axis of symmetry, and intercepts. Plot these points and draw a smooth curve through them.

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What is the discriminant in a quadratic equation?

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The solutions are the points where the two equations intersect: (-4, -1) and (2, 5).