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 'a' in the vertex form of a quadratic equation represent?

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

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

Back

To find the vertex from the standard form y = ax² + bx + c, use the formula h = -b/(2a) and k = f(h), where f(h) is the value of the quadratic at x = h.

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. It can be found using the formula x = h, where (h, k) is the vertex.

Front

Convert the quadratic equation y = x² + 6x + 8 to vertex form.

Back

y = (x + 3)² - 1.

Front

What is the vertex of the quadratic function y = -2(x + 1)² + 3?

Back

The vertex is (-1, 3).

Front

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

Back

The direction of the parabola is determined by the sign of 'a'. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

Write the quadratic equation y = 3x² - 12x + 7 in vertex form.

Back

y = 3(x - 2)² - 5.

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 can you find the x-intercepts of a quadratic function?

Back

To find the x-intercepts, set y = 0 and solve the quadratic equation ax² + bx + c = 0.