Vertex Form

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is given by y = 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 indicates the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

How do you find the vertex from the vertex form equation y = a(x - h)² + k?

Back

The vertex is the point (h, k) in the equation.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, dividing it into two mirror-image halves.

Front

How do you determine the roots of a quadratic equation in vertex form?

Back

To find the roots, set y = 0 and solve for x in the equation y = a(x - h)² + k.

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it has a maximum point at the vertex, and the 'a' value in the vertex form is negative.

Front

What is the relationship between the vertex and the maximum/minimum of a parabola?

Back

The vertex represents the maximum point if the parabola opens downwards and the minimum point if it opens upwards.

Front

How can you identify the vertex from the equation y = 3(x + 5)² - 4?

Back

The vertex is (-5, -4) because it is in the form y = a(x - h)² + k.

Front

What is the formula to convert standard form to vertex form?

Back

To convert from standard form (y = ax² + bx + c) to vertex form, complete the square.