Linear / Quadratic Systems of Equations

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What is a linear equation?

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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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is a quadratic equation?

Back

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

Front

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 graphs of the equations. If they intersect at two points, there are two solutions; if they touch at one point, there is one solution; and if they do not intersect, there are no solutions.

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CCSS.HSA.REI.C.7

Front

What is the substitution method in solving systems of equations?

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

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for a system of equations to have no solution?

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A system of equations has no solution when the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

Front

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 whether it opens upwards or downwards. It can be found using the formula (-b/2a, f(-b/2a)).

Front

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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CCSS.HSF-IF.C.7A

Front

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: if positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

Tags

CCSS.HSA-REI.B.4B

Front

What is the difference between a linear function and a quadratic function?

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A linear function has a constant rate of change and graphs as a straight line, while a quadratic function has a variable rate of change and graphs as a parabola.

Front

What is the standard form of a quadratic equation?

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The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.