Quadratic Equations Practice

Front

What is the discriminant in a quadratic equation and what does it indicate about the number of real solutions?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. If it is greater than zero, there are two real solutions; if it is equal to zero, there is one real solution; if it is less than zero, there are no real solutions.

Front

What does the term 'roots' refer to in the context of quadratic equations?

Back

Roots are the values of x that make the quadratic equation equal to zero. They are also known as x-intercepts or zeros.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, depending on whether it opens upwards or downwards.

Front

What does the 'c' in the quadratic equation y = ax² + bx + c represent?

Back

The 'c' represents the y-intercept of the quadratic function, which is the point where the graph intersects the y-axis.

Front

How do you multiply two binomials using the FOIL method?

Back

FOIL stands for First, Outside, Inside, Last. Multiply the first terms, then the outside terms, then the inside terms, and finally the last terms, and combine like terms.

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. It can be found using the formula x = -b/(2a).

Front

What is the difference between a maximum and minimum value in a quadratic function?

Back

A maximum value is the highest point of the parabola (when it opens downwards), while a minimum value is the lowest point (when it opens upwards).

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 and a ≠ 0.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

If the coefficient 'a' in the quadratic equation y = ax² + bx + c is positive, the parabola opens upwards. If 'a' is negative, it opens downwards.

Front

What are x-intercepts and how are they related to quadratic equations?

Back

X-intercepts are the points where the graph of the quadratic function crosses the x-axis. They are the solutions to the equation when y = 0.