9.5 - Solving systems with linear and quadratic functions

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What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

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What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form y = ax^2 + bx + c, where a, b, and c are constants.

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How do you find the intersection of a linear and a quadratic function?

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To find the intersection, set the equations equal to each other and solve for x. Then substitute x back into either equation to find y.

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

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A point is a solution if it satisfies all equations in the system, meaning it makes all equations true when substituted.

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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, found using the formula x = -b/(2a).

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What is the discriminant in a quadratic equation?

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The discriminant is the part of the quadratic formula under the square root, given by b^2 - 4ac. It determines the nature of the roots.

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What does a positive discriminant indicate?

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A positive discriminant indicates that the quadratic equation has two distinct real roots.

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What does a negative discriminant indicate?

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A negative discriminant indicates that the quadratic equation has no real roots, only complex roots.

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What does a zero discriminant indicate?

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A zero discriminant indicates that the quadratic equation has exactly one real root, also known as a repeated root.