Solving Quadratic Linear Systems

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What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

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What is a linear equation?

Back

A linear equation is an equation of the first degree, which means it can be written in the form ax + b = 0, where a and b are constants.

Front

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 substitution in solving equations?

Back

Substitution is a method of solving a system of equations by solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the graphical representation of a quadratic equation?

Back

The graphical representation of a quadratic equation is a parabola, which can open upwards or downwards depending on the sign of the leading coefficient.

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How can 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 intersection points of the linear and quadratic graphs. They can intersect at 0, 1, or 2 points.

Front

What is the vertex of a parabola?

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The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

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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 (b² - 4ac) that determines the nature of the roots: if positive, there are 2 real solutions; if zero, 1 real solution; if negative, no real solutions.

Front

What is the standard form of a quadratic equation?

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The standard form of a quadratic equation is y = ax² + bx + c.

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What is the factored form of a quadratic equation?

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The factored form of a quadratic equation is y = a(x - r1)(x - r2), where r1 and r2 are the roots of the equation.