Parabolas in Standard Form

Front

What is the parent function of all quadratic functions?

Back

The parent function of all quadratic functions is y = x².

Front

In which direction does the parabola y = -2x² - 4x + 1 open?

Back

The parabola opens down.

Front

How do you determine the direction a parabola opens based on its leading coefficient?

Back

If the leading coefficient (a) is positive, the parabola opens up; if it is negative, the parabola opens down.

Front

What is the vertex of the parabola y = -2x² - 4x + 1?

Back

The vertex is (-1, 3).

Front

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

Back

The vertex (h, k) can be found using the formula h = -b/(2a) and k = f(h), where f(x) is the quadratic function.

Front

What is the vertex of the parabola y = x² - 2x + 4?

Back

The vertex is (1, 3).

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c.

Front

What do the coefficients a, b, and c represent in the standard form of a quadratic function?

Back

In the standard form y = ax² + bx + c, 'a' determines the direction and width of the parabola, 'b' affects the position of the vertex, and 'c' is the y-intercept.

Front

How does the value of 'a' affect the width of a parabola?

Back

The larger the absolute value of 'a', the narrower the parabola; the smaller the absolute value of 'a', the wider the parabola.

Front

What is the significance of the vertex in a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens up or down.