Solving Quadratics by graphing

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does it mean for a function to have zeros?

Back

Zeros of a function are the values of x for which the function's output is zero. They are the x-intercepts of the graph.

Front

How can you find the zeros of a quadratic function graphically?

Back

You can find the zeros of a quadratic function by identifying the points where the graph intersects the x-axis.

Front

What are x-intercepts?

Back

X-intercepts are the points where the graph of a function crosses the x-axis, corresponding to the zeros of the function.

Front

What is the vertex of a quadratic function?

Back

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

Front

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

Back

A maximum is the highest point on the graph of a quadratic function (when it opens downwards), while a minimum is the lowest point (when it opens upwards).

Front

How many solutions can a quadratic equation have?

Back

A quadratic equation can have two solutions, one solution, or no real solutions, depending on the discriminant (b² - 4ac).

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula, which determines the nature and number of solutions.

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real solutions.

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, the quadratic equation has exactly one real solution (a repeated root).