3-1 Key Features of Parabolas

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 mirror-image halves. It passes through the vertex.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It is the point where the parabola changes direction.

Front

How do you find the y-intercept of a parabola?

Back

The y-intercept is found by evaluating the quadratic equation at x = 0. It is the point where the parabola crosses the y-axis.

Front

What are x-intercepts (roots) of a parabola?

Back

X-intercepts are the points where the parabola crosses the x-axis. They can be found by solving the quadratic equation for when y = 0.

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it means that the vertex is the minimum point, and the arms of the parabola extend upwards.

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it means that the vertex is the maximum point, and the arms of the parabola extend downwards.

Front

How can you determine the number of x-intercepts a parabola has?

Back

The number of x-intercepts can be determined by the discriminant (b² - 4ac) of the quadratic equation. If it's positive, there are 2 intercepts; if zero, 1 intercept; if negative, none.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.

Front

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

Back

The coefficient 'a' determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

Front

How do you find the maximum or minimum value of a parabola?

Back

The maximum or minimum value can be found at the vertex of the parabola. The y-coordinate of the vertex gives this value.