Solve Quadratic Equations

Front

What is a quadratic equation?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: D > 0 means 2 real roots, D = 0 means 1 real root, and D < 0 means no real roots.

Front

How do you find the roots of a quadratic equation using the Quadratic Formula?

Back

The roots can be found using the formula x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the vertex of a parabola represented by a quadratic equation?

Back

The vertex is the highest or lowest point of the parabola, found at the point (h, k) where h = -b/(2a) and k = f(h).

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, given by the equation x = -b/(2a).

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis, found by solving the equation ax² + bx + c = 0.

Front

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

Back

The coefficient 'a' determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What does it mean if a quadratic equation has no real solutions?

Back

It means the graph of the quadratic function does not intersect the x-axis, which occurs when the discriminant is negative.

Front

How can you determine the number of real solutions from the discriminant?

Back

If the discriminant is positive, there are 2 real solutions; if it is zero, there is 1 real solution; if it is negative, there are no real solutions.