Solving Quadratics Review

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

Identify the values of a, b, and c in the equation 4x² - 8x = 3.

Back

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

Front

What are the solutions for x in the equation (x + 2)(x - 3) = 0?

Back

x = -2 and x = 3.

Front

Solve for x: x² = 16.

Back

x = ±4.

Front

Factor the quadratic expression x² - 11x + 24.

Back

(x - 3)(x - 8).

Front

What does it mean for a quadratic equation to have real solutions?

Back

A quadratic equation has real solutions if its discriminant (b² - 4ac) is greater than or equal to zero.

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.

Front

How do you find the axis of symmetry for a quadratic equation in standard form?

Back

The axis of symmetry can be found using the formula x = -b/(2a).

Front

What is the quadratic formula?

Back

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

Front

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

Back

The discriminant determines the nature of the roots: if positive, two distinct real roots; if zero, one real root; if negative, no real roots.