Algebra 1 - Ch. 9.6 Solving Nonlinear Systems of Equations Pg534

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What is a nonlinear system of equations?

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A nonlinear system of equations is a set of equations in which at least one equation is not linear, meaning it cannot be represented as a straight line on a graph.

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How do you solve a system of equations by graphing?

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To solve a system of equations by graphing, plot each equation on the same set of axes and identify the point(s) where the graphs intersect. These intersection points represent the solutions.

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What does it mean if a system of equations has no solution?

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A system of equations has no solution if the graphs of the equations do not intersect, indicating that there are no values that satisfy all equations simultaneously.

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What is the vertex of a quadratic function?

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What is the significance of the zeros of a quadratic function?

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The zeros of a quadratic function are the x-values where the function equals zero. They represent the points where the graph intersects the x-axis.

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How can you determine the number of solutions in a nonlinear system?

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The number of solutions in a nonlinear system can be determined by analyzing the graphs of the equations: 0 solutions (no intersection), 1 solution (tangent), or 2 solutions (two intersection points).

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What is the standard form of a quadratic equation?

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What does the discriminant of a quadratic equation tell us?

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What is the process to find the intersection of two curves algebraically?

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To find the intersection of two curves algebraically, set the equations equal to each other and solve for the variable. Substitute back to find the corresponding values.

Front

What is a parabola?

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