Vertex Form Quadratics

Front

What is the vertex form of a quadratic function?

Back

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

Front

What does the 'a' value in the vertex form indicate?

Back

The 'a' value determines the direction the parabola opens: if 'a' is positive, it opens upward; if 'a' is negative, it opens downward.

Front

How does changing the 'h' value in the vertex form affect the graph?

Back

Changing the 'h' value shifts the graph horizontally. If 'h' increases, the graph shifts to the right; if 'h' decreases, it shifts to the left.

Front

How does changing the 'k' value in the vertex form affect the graph?

Back

Changing the 'k' value shifts the graph vertically. If 'k' increases, the graph shifts up; if 'k' decreases, it shifts down.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = h in vertex form.

Front

What is the significance of the vertex in a parabola?

Back

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

Front

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

Back

To find the vertex from standard form f(x) = ax² + bx + c, use the formula h = -b/(2a) and then calculate k by substituting h back into the function.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph crosses the x-axis, found by solving the equation f(x) = 0.

Front

What is the relationship between the vertex and the axis of symmetry?

Back

The vertex lies on the axis of symmetry, which is the line that passes through the vertex and divides the parabola into two equal halves.

Front

How can you determine if a parabola opens upward or downward?

Back

If the 'a' value in the vertex form f(x) = a(x-h)² + k is positive, the parabola opens upward; if 'a' is negative, it opens downward.