Forms of Quadratics Review

Front

What is the factored form of a quadratic equation?

Back

A quadratic equation in factored form is expressed as y = a(x - r1)(x - r2), where r1 and r2 are the roots (zeros) of the equation.

Front

What are the x-intercepts of the quadratic equation y = 3(x - 6)(x + 3)?

Back

The x-intercepts are (6, 0) and (-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 zeros of the quadratic function f(x) = (x + 1)(x + 5)?

Back

Set f(x) = 0: (x + 1)(x + 5) = 0. The zeros are x = -1 and x = -5.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c, where a, b, and c are constants.

Front

What does the vertex of a parabola represent?

Back

The vertex is the highest or lowest point of the parabola, depending on the direction it opens.

Front

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

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

How can you convert from standard form to vertex form?

Back

Use the method of completing the square to rewrite the equation in the form y = a(x - h)² + k.

Front

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

Back

For a quadratic equation ax² + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is the vertical line x = -b/(2a) that divides the parabola into two mirror-image halves.