Quadratics Practice

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 y = ax² + bx + c.

Front

What does the discriminant tell us about a quadratic equation?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: D > 0 means 2 real solutions, D = 0 means 1 real solution, and D < 0 means 2 complex solutions.

Front

How do you calculate the discriminant of the quadratic equation 2x² - x + 8?

Back

D = (-1)² - 4(2)(8) = 1 - 64 = -63.

Front

What are the zeros of a quadratic equation?

Back

The zeros (or roots) of a quadratic equation are the values of x that make the equation equal to zero.

Front

How do you find the zeros of the quadratic equation x² - 4x = 0?

Back

Factor the equation: x(x - 4) = 0. The zeros are x = 0 and x = 4.

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.

Front

How do you find the vertex of the quadratic function y = 2x² + 4x + 1?

Back

The vertex can be found using the formula x = -b/(2a). Here, x = -4/(2*2) = -1. Substitute x = -1 into the equation to find y.

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

Front

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

Back

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