Quadratics

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the 'a' value in a quadratic equation determine?

Back

The 'a' value determines the direction of the parabola: if 'a' is positive, the parabola opens upwards and has a minimum value; if 'a' is negative, it opens downwards and has a maximum value.

Front

What is the vertex of a parabola?

Back

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

Front

How do you find the vertex of a quadratic equation in standard form?

Back

The vertex (h, k) can be found using the formula h = -b/(2a) and k = f(h), where f(x) is the quadratic function.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.

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 value of the discriminant (b² - 4ac).

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac that determines the nature of the roots of the quadratic equation.

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real solutions.

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that the quadratic equation has exactly one real solution (a repeated root).

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that the quadratic equation has no real solutions, only complex solutions.