Quadratic Basics

Front

What are the solutions of a quadratic equation?

Back

The solutions of a quadratic equation are the values of x that make the equation equal to zero, also known as the roots or zeros of the equation.

Front

How can you determine the number of solutions a quadratic equation has from its graph?

Back

The number of solutions can be determined by the number of times the graph intersects the x-axis: 0 intersections means no solutions, 1 intersection means one solution, and 2 intersections mean two solutions.

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 does it mean for a quadratic function to have a minimum value?

Back

A quadratic function has a minimum value if its graph opens upwards, indicating that the vertex is the lowest point on the graph.

Front

What does it mean for a quadratic function to have a maximum value?

Back

A quadratic function has a maximum value if its graph opens downwards, indicating that the vertex is the highest point on the graph.

Front

How do you find the range of a quadratic function?

Back

The range of a quadratic function can be determined by the vertex and the direction the parabola opens. If it opens upwards, the range starts from the y-coordinate of the vertex to positive infinity; if it opens downwards, it starts from negative infinity to the y-coordinate of the vertex.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What is the significance of the coefficient 'a' in a quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts of a quadratic function are the points where the graph intersects the x-axis, corresponding to the solutions of the equation.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, passing through the vertex.