Parabolas Standard/Vertex Form

Front

What is the standard form of a parabola?

Back

The standard form of a parabola is given by the equation y = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the vertex form of a parabola?

Back

The vertex form of a parabola is given by the equation y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Front

How can you determine if a parabola opens up or down?

Back

A parabola opens up if the coefficient 'a' in the equation y = ax^2 + bx + c is positive. It opens down if 'a' is negative.

Front

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

Back

The vertex of the parabola is (3, 5).

Front

How do you find the x-coordinate of the vertex in standard form?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a) from the standard form y = ax^2 + bx + c.

Front

What is the axis of symmetry for the parabola y = -x^2 + 4x - 3?

Back

The axis of symmetry is x = -b/(2a) = 4/(-2) = 2.

Front

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

Back

The 'a' value affects the width and direction of the parabola. A larger absolute value of 'a' makes the parabola narrower, while a smaller absolute value makes it wider.

Front

What is the y-intercept of the parabola y = x^2 - 4?

Back

The y-intercept is the point where x = 0. For this parabola, y = 0^2 - 4 = -4, so the y-intercept is (0, -4).

Front

How do you convert from standard form to vertex form?

Back

To convert from standard form to vertex form, you can complete the square.

Front

What is the minimum value of the parabola y = 3(x + 2)^2 - 1?

Back

The minimum value occurs at the vertex, which is -1.