Linear and quadratic systems

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the second degree, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

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What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the substitution method in solving systems of equations?

Back

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

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What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane.

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What is the vertex of a quadratic function?

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The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola.

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How do you find the x-intercepts of a quadratic equation?

Back

To find the x-intercepts of a quadratic equation, set y = 0 and solve the resulting equation for x.

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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 b² - 4ac, which determines the nature of the roots.

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What does it mean if the discriminant is positive?

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If the discriminant is positive, the quadratic equation has two distinct real roots.

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What does it mean if the discriminant is zero?

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If the discriminant is zero, the quadratic equation has exactly one real root, also known as a repeated or double root.