ENH CIA #8 - Vertex Form

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you find the maximum height of a projectile described by a quadratic function?

Back

To find the maximum height, determine the vertex of the quadratic function, which occurs at x = -b/(2a) for the standard form ax² + bx + c.

Front

What does the 'a' value in the vertex form of a quadratic function indicate?

Back

The 'a' value indicates 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 a quadratic function from standard form to vertex form?

Back

You can convert by completing the square on the quadratic expression.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as (x - a)² = x² - 2ax + a².

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

How do you determine the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form ax² + bx + c.

Front

What transformation occurs when a quadratic function is reflected across the x-axis?

Back

When reflected across the x-axis, the 'a' value in the function changes from positive to negative, inverting the parabola.

Front

What does shifting a quadratic function 3 units left look like in vertex form?

Back

Shifting 3 units left changes the vertex form from f(x) = a(x - h)² + k to f(x) = a(x + 3)² + k.

Front

How do you find the time it takes for a projectile to reach its maximum height?

Back

The time to reach maximum height can be found using the formula t = -b/(2a) from the height function in standard form.