Quadratic Formula

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of the quadratic equation ax² + bx + c = 0.

Front

What does the 'a' represent in the quadratic equation ax² + bx + c = 0?

Back

'a' is the leading coefficient, which determines the direction of the parabola (upward if a > 0, downward if a < 0).

Front

What does the 'b' represent in the quadratic equation ax² + bx + c = 0?

Back

'b' is the coefficient of the x term, which affects the position of the vertex of the parabola.

Front

What does the 'c' represent in the quadratic equation ax² + bx + c = 0?

Back

'c' is the constant term, which represents the y-intercept of the parabola.

Front

How do you convert the equation 4x² – 8x = 3 into standard form?

Back

Subtract 3 from both sides to get 4x² - 8x - 3 = 0.

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 of the parabola.

Front

How do you find the vertex of a parabola given in standard form?

Back

The vertex can be found using the formula h = -b/(2a) and k = f(h), where f(h) is the value of the function at x = h.

Front

What is the discriminant in the quadratic formula?

Back

The discriminant is b² - 4ac, which determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What are the roots of the equation x² + 4x - 40 = -8?

Back

The roots are x = -8 and x = 4.

Front

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

Back

The leading coefficient 'a' determines the width and direction of the parabola.