Linear / Quadratic Systems of Equations

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.

Front

What is a quadratic equation?

Back

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

Front

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

Back

A system of equations has no solution when the lines represented by the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have one solution?

Back

A system of equations has one solution when the lines represented by the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have two solutions?

Back

A system of equations has two solutions when the quadratic graph intersects the linear graph at two distinct points.

Front

How do you solve a system of linear and quadratic equations?

Back

You can solve a system of linear and quadratic equations using substitution or elimination methods.

Front

What is the vertex of a parabola?

Back

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

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a) for the quadratic equation ax² + bx + c.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 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.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.