Finding Zeros of Quadratics

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x for which the function equals zero (y = 0). They are also known as the roots of the equation.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

How do you determine the number of real roots of a quadratic equation?

Back

The number of real roots can be determined using the discriminant (D = b² - 4ac). If D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

What does it mean if a quadratic has two distinct real roots?

Back

It means the graph of the quadratic function intersects the x-axis at two points.

Front

What does it mean if a quadratic has one real root?

Back

It means the graph of the quadratic function touches the x-axis at one point (the vertex) and does not cross it.

Front

What does it mean if a quadratic has no real roots?

Back

It means the graph of the quadratic function does not intersect the x-axis at all.

Front

How can you find the zeros of the quadratic equation y = x² - 2x - 24?

Back

Use the quadratic formula: x = (2 ± √(2² - 4(1)(-24))) / (2*1) = 6, -4.

Front

What are the roots of the equation y = x² - x - 20?

Back

The roots are found using the quadratic formula: x = (1 ± √(1² - 4(1)(-20))) / (2*1) = 5, -4.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of the quadratic function, located at x = -b/(2a).