Mastering the Quadratic Formula

What is the quadratic formula?

• x = (b ± √(4ac - b²)) / (2a)

• x = (-b ± 2√(b² - 4ac)) / a

• x = (-b ± √(b² - 4ac)) / (2a)

• x = (b ± √(b² + 4ac)) / (2a)

Given the equation x² + 2x - 3, identify a, b, and c.

• a = 1, b = -2, c = 3

• a = 2, b = 3, c = -1

• a = 1, b = 2, c = -3

• a = 0, b = 1, c = 3

Apply the quadratic formula to find the roots of x² + 2x - 3.

• The roots are x = 3 and x = -1.

• The roots are x = 2 and x = -1.

• The roots are x = 1 and x = -3.

• The roots are x = 0 and x = -3.

What are the steps to derive the quadratic formula?

• x = (b ± √(b^2 + 4ac)) / (2a)

• x = (b ± 2√(ac)) / (a + c)

• x = (2a ± b) / √(b^2 - 4ac)

• x = (-b ± √(b^2 - 4ac)) / (2a)

How many solutions can a quadratic equation have?

• 0, 1, or 2 solutions

• 3 solutions

• Only 1 solution

• Infinitely many solutions

If the discriminant is positive, what does that indicate about the roots?

• The roots are complex numbers.

• The roots are two distinct real numbers.

• The roots are identical real numbers.

• The roots are imaginary numbers.

Calculate the discriminant for the equation x² + 2x - 3.

• 0

• 16

• 4

• 10

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

• The vertex indicates the maximum or minimum value of the quadratic function.

• The vertex indicates the direction of the parabola's opening.

• The vertex represents the roots of the quadratic equation.

• The vertex is the point where the graph intersects the y-axis.

Explain how to graph the quadratic function y = x² + 2x - 3.

• The vertex is at (0, 0) and the parabola opens downwards.

• The graph of the quadratic function y = x² + 2x - 3 is a parabola with vertex at (-1, -4), y-intercept at (0, -3), and x-intercepts at (-3, 0) and (1, 0).

• The x-intercepts are at (-2, 0) and (2, 0).

• The graph is a straight line with a slope of 2.

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

• The sum of the roots is a/b and the product of the roots is -c/a.

• The sum of the roots is -b/a and the product of the roots is c/a.

• The sum of the roots is -a/b and the product of the roots is c/b.

• The sum of the roots is b/a and the product of the roots is -c/b.