Quadratic formula with imaginary solutions

Front

What are the coefficients a, b, and c in the quadratic equation 2x^2 - 3x - 5 = 0?

Back

a = 2, b = -3, c = -5

Front

How do you convert the quadratic equation y = x^2 + 14x + 50 to vertex form?

Back

y = (x + 7)^2 + 1

Front

What is the solution to the equation x^2 + 4x - 16 = 0 using the quadratic formula?

Back

x = -2 ± 2√5

Front

How do you find the zeros of the function f(x) = (x + 3)^2 - 4?

Back

The zeros are -5 and -1.

Front

What is the quadratic formula?

Back

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Front

What does it mean if a quadratic equation has imaginary solutions?

Back

It means the discriminant (b^2 - 4ac) is less than zero.

Front

How do you determine if a quadratic equation has real or imaginary solutions?

Back

Calculate the discriminant (b^2 - 4ac). If it's positive, there are two real solutions; if zero, one real solution; if negative, two imaginary solutions.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form is y = a(x - h)^2 + k, where (h, k) is the vertex.

Front

How do you complete the square for the equation x^2 + 4x - 16?

Back

Add and subtract (4/2)^2 = 4 to rewrite it as (x + 2)^2 - 20 = 0.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola.