Solving quadratics

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) determines the nature of the roots: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means no real roots.

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, express the quadratic in the form (px + q)(rx + s) = 0, then set each factor to zero and solve for x.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, found at the point (h, k) in the vertex form y = a(x - h)² + k.

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 maximum height of a projectile?

Back

The maximum height of a projectile can be found using the vertex of the quadratic equation that models its height over time.

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 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 is the relationship between the roots and the coefficients of a quadratic equation?

Back

For a quadratic equation ax² + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a.