Quadratics Review

Front

What is the factored form of the quadratic expression x² + 5x - 24?

Back

(x + 8)(x - 3)

Front

What is the standard form of a quadratic equation?

Back

y = ax² + bx + c

Front

If the length of a rectangle is 4 inches more than its width and the perimeter is 96 inches, how do you find the dimensions?

Back

Set up the equations: 2(width) + 2(width + 4) = 96, solve for width and length.

Front

How do you determine the time it takes for an object to hit the ground when modeled by a quadratic function?

Back

Set the function equal to zero and solve for t.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is given by the formula x = -b/(2a) for the quadratic equation ax² + bx + c.

Front

What does the vertex of a parabola represent in a quadratic function?

Back

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

Front

How can you find the roots of a quadratic equation?

Back

Use factoring, completing the square, or the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: two real and distinct, one real and repeated, or no real roots.

Front

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

Back

Use the method of completing the square.

Front

What is the formula for the perimeter of a rectangle?

Back

Perimeter = 2(length + width).