QUADRATIC EQUATIONS

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in 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: if D > 0, there are two distinct real roots; if D = 0, there is one real root (equal roots); if D < 0, there are no real roots.

Front

What are the roots of the equation 64x² - 1 = 0?

Back

The roots are x = ±1/8.

Front

How do you find the roots of a quadratic equation in the form ax² + bx = 0?

Back

Factor out x: x(ax + b) = 0, giving roots x = 0 and x = -b/a.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, found at the point (-b/2a, f(-b/2a)).

Front

What does it mean for a quadratic equation to have equal roots?

Back

Equal roots occur when the discriminant is zero (D = 0), indicating that the parabola touches the x-axis at one point.

Front

Can 0 be a root of a quadratic equation?

Back

Yes, 0 can be a root if the equation can be factored to include x as a factor.

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 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.