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 vertex form of a quadratic equation?

Back

The vertex can be found directly from the vertex form y = a(x - h)² + k as the point (h, k).

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

How do you convert standard form to vertex form?

Back

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

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

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

Back

y = 2(x + 2)² - 2.

Front

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

Back

y = 3(x - 2)² - 5.

Front

What are the roots of a quadratic equation?

Back

The roots (or x-intercepts) are the values of x where the quadratic function equals zero.

Front

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

Back

Set y = 0 and solve for x in the equation y = a(x - h)² + k.