Quadratic Formula

Front

What is the quadratic formula?

Back

The quadratic formula is given by x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients of the quadratic equation ax² + bx + c = 0.

Front

What are the coefficients in a quadratic equation?

Back

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

Front

How do you identify a, b, and c in the equation x² - 6x + 14?

Back

In the equation x² - 6x + 14, a = 1, b = -6, and c = 14.

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 is positive, there are two distinct real roots; if it is zero, there is one real root (a repeated root); if it is negative, there are no real roots (the roots are complex).

Front

How do you solve the quadratic equation 8x² - 6x = -1?

Back

First, rearrange to 8x² - 6x + 1 = 0. Then apply the quadratic formula with a = 8, b = -6, c = 1.

Front

What are the roots of the quadratic equation x² + 4x + 3 = 0?

Back

The roots can be found using the quadratic formula: x = (-4 ± √(4² - 4*1*3)) / (2*1) = -1 and -3.

Front

What is the significance of the '±' symbol in the quadratic formula?

Back

The '±' symbol indicates that there are two possible solutions for x, one for addition and one for subtraction.

Front

How do you find the vertex of a parabola represented by a quadratic equation?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))) where f(x) is the quadratic function.

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.

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert to vertex form, use the method of completing the square: y = a(x - h)² + k, where (h, k) is the vertex.