Quadratic Formula - Post-Test

Front

What is the standard form of a quadratic equation?

Back

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

Front

What are the values of a, b, and c in the equation 4x² - 8x = 3?

Back

a = 4, b = -8, c = -3.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

Front

How do you identify the coefficients a, b, and c in the quadratic formula?

Back

In the quadratic equation ax² + bx + c = 0, a is the coefficient of x², b is the coefficient of x, and c is the constant term.

Front

What does the discriminant (b² - 4ac) tell us about the roots of a quadratic equation?

Back

The discriminant indicates the nature of the roots: if it's positive, there are two distinct real roots; if it's zero, there is one real root (a repeated root); if it's negative, there are two complex roots.

Front

How do you solve the quadratic equation x² + 6x - 16 = 0 using the quadratic formula?

Back

Plugging into the quadratic formula gives x = (-6 ± √(6² - 4(1)(-16))) / (2(1)).

Front

What are the roots of the equation 2x² + 2 = 9x?

Back

The roots are x = (9 ± √65) / 4.

Front

What is the significance of complex roots in a quadratic equation?

Back

Complex roots indicate that the quadratic does not intersect the x-axis and thus has no real solutions.

Front

How do you find the missing number in the quadratic formula for the equation 2x² + 2x - 12 = 0?

Back

The missing number is the coefficient of x, which is 2.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.