Forms of Quadratics Review

Front

What are the zeros of the function f(x) = (x + 7)(x + 5)?

Back

The zeros are (-7, 0) and (-5, 0).

Front

Does the graph of a quadratic function have a maximum or minimum value?

Back

It can have either a maximum or minimum value depending on the direction of the parabola. If it opens upwards, it has a minimum value; if it opens downwards, it has a maximum value.

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

What form is the quadratic function f(x) = (x - 8)(x + 3) in?

Back

It is in Factor Form with zeros at x = 8 and x = -3.

Front

What form is the equation y = 2(x - 3)² - 2 in?

Back

It is in Vertex Form with the vertex at (3, -2).

Front

How do you find the vertex of a quadratic function in standard form?

Back

For a quadratic in standard form y = ax² + bx + c, the vertex can be found using the formula x = -b/(2a).

Front

What is the axis of symmetry (AOS) for a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror images, given by the equation x = -b/(2a) for the standard form.

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 it mean for a quadratic function to have real zeros?

Back

A quadratic function has real zeros if its graph intersects the x-axis, which occurs when the discriminant (b² - 4ac) is greater than or equal to zero.

Front

How can you determine if a quadratic opens upwards or downwards?

Back

A quadratic opens upwards if the leading coefficient (a) is positive and downwards if it is negative.