Parts of a Parabola

Front

What are the roots of a parabola?

Back

The roots of a parabola are the x-values where the parabola intersects the x-axis. For example, in the equation y = (x-0)(x-4), the roots are 0 and 4.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two equal halves. It passes through the vertex of the parabola.

Front

Where is the vertex of a parabola located?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. For example, in the vertex form y = a(x-h)² + k, the vertex is at the point (h, k).

Front

What are the solutions of a quadratic equation?

Back

The solutions of a quadratic equation are the values of x that make the equation equal to zero. They can be found using factoring, completing the square, or the quadratic formula.

Front

What is the y-intercept of a parabola?

Back

The y-intercept is the point where the parabola intersects the y-axis. It can be found by setting x = 0 in the equation of the parabola.

Front

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

Back

For a parabola in standard form y = ax² + bx + c, the vertex can be found using the formula x = -b/(2a) and then substituting this x-value back into the equation to find the y-coordinate.

Front

What does the term 'concave up' mean in relation to a parabola?

Back

A parabola is concave up if it opens upwards, meaning the vertex is the minimum point. This occurs when the coefficient 'a' in the equation y = ax² + bx + c is positive.

Front

What does the term 'concave down' mean in relation to a parabola?

Back

A parabola is concave down if it opens downwards, meaning the vertex is the maximum point. This occurs when the coefficient 'a' in the equation y = ax² + bx + c is negative.

Front

How can you determine the direction a parabola opens?

Back

The direction a parabola opens can be determined by the sign of the coefficient 'a' in the equation y = ax² + bx + c. If 'a' is positive, it opens upwards; if 'a' is negative, it opens downwards.

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.