Parabolas Flashcard

Front

What is the standard form of a parabola?

Back

The standard form of a parabola is given by the equation y = a(x - h)² + k, where (h, k) is the vertex of the parabola and 'a' determines the direction and width of the parabola.

Front

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

Back

To find the vertex of a parabola in standard form y = a(x - h)² + k, the vertex is the point (h, k).

Front

What does the value of 'a' in the parabola equation indicate?

Back

The value of 'a' indicates the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards. The absolute value of 'a' affects the width of the parabola.

Front

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

Back

The vertex of the parabola y = x² - 4x + 1 is (2, -3).

Front

How do you convert the equation of a parabola from standard form to vertex form?

Back

To convert from standard form y = ax² + bx + c to vertex form y = a(x - h)² + k, complete the square on the quadratic expression.

Front

What is the maximum or minimum value of a parabola?

Back

The maximum or minimum value of a parabola occurs at its vertex. If the parabola opens upwards, it has a minimum value; if it opens downwards, it has a maximum value.

Front

How do you solve a quadratic equation in factored form, such as (2x - 1)(x + 4) = 0?

Back

To solve a quadratic equation in factored form, set each factor equal to zero: 2x - 1 = 0 and x + 4 = 0, then solve for x.

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of a quadratic equation: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

How can you find a quadratic model for a set of data points?

Back

To find a quadratic model for a set of data points, use regression analysis to fit a quadratic equation of the form s = at² + bt + c to the data.