CW Solving Quadratics by Graphing

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 does the graph of a quadratic equation look like?

Back

The graph of a quadratic equation is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

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 the direction it opens.

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 formula x = -b/(2a).

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.

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).

Front

What does it mean if the discriminant is negative?

Back

If the discriminant is negative, the quadratic equation has no real solutions, only complex solutions.

Front

How can you find the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by setting the quadratic equation equal to zero and solving for x.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.