Writing Quadratics in 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 axis of symmetry represent in a parabola?

Back

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

Front

How do you find the vertex of a parabola given in standard form?

Back

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

Front

What is the significance of the 'a' value in the vertex form of a quadratic?

Back

The 'a' value determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

Front

Convert the equation y = 2x² + 8x + 6 into vertex form.

Back

y = 2(x + 2)² - 2.

Front

What is the vertex of the parabola given by y = -3(x + 1)² + 5?

Back

The vertex is (-1, 5).

Front

How do you determine the direction of a parabola from its equation?

Back

The direction of a parabola is determined by the sign of 'a' in the vertex form. Positive 'a' opens upwards, while negative 'a' opens downwards.

Front

What are the x-intercepts of a parabola?

Back

The x-intercepts are the points where the parabola crosses the x-axis, found by setting y = 0 and solving for x.

Front

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

Back

The formula involves completing the square: y = a(x - h)² + k.

Front

What does the term 'completing the square' mean?

Back

Completing the square is a method used to convert a quadratic equation into vertex form by adding and subtracting the same value.