Quadratic Linear Systems

Front

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.

Front

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 y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

A system of equations has two solutions when the graphs of the equations intersect at two distinct points.

Front

How can you determine the number of solutions in a quadratic-linear system?

Back

You can determine the number of solutions by analyzing the intersection points of the quadratic and linear graphs. This can be done graphically or algebraically.

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 discriminant in a quadratic equation?

Back

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 two real solutions; if zero, one real solution; if negative, no real solutions.

Front

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

Back

A system of equations has no solution when the graphs of the equations are parallel and never intersect.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the graph of the equation crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

How do you find the intersection of a quadratic and a linear equation?

Back

To find the intersection, set the equations equal to each other and solve for x, then substitute back to find y.

Front

What is a parabola?

Back

A parabola is the graph of a quadratic function, which is U-shaped and can open upwards or downwards.