4.7 Flashcard review

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on its orientation. For example, the vertex of the parabola represented by the equation y = x^2 is (0,0).

Front

What is the equation for the axis of symmetry of a parabola?

Back

The axis of symmetry of a parabola is a vertical line that divides the parabola into two mirror-image halves. It can be expressed as x = h, where (h,k) is the vertex of the parabola.

Front

What is the green dashed line in a parabola called?

Back

The green dashed line is called the line of symmetry, which is the axis of symmetry for the parabola.

Front

What is the vertex form of a parabola?

Back

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

Front

How do you find the vertex of a quadratic function in standard form?

Back

To find the vertex of a quadratic function in standard form y = ax^2 + bx + c, use the formula h = -b/(2a) and then substitute h back into the equation to find k.

Front

What are the roots or x-intercepts of a parabola?

Back

The roots or x-intercepts of a parabola are the points where the graph intersects the x-axis, found by solving the equation y = 0.

Front

What is the significance of the coefficient 'a' in the quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola's opening: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What does the term 'discriminant' refer to in a quadratic equation?

Back

The discriminant, given by the formula D = b^2 - 4ac, determines the nature of the roots of the quadratic equation ax^2 + bx + c = 0.

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real roots.

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, the quadratic equation has exactly one real root, also known as a repeated or double root.