What makes a parabola open upward

In this case the vertex is the minimum, or lowest point, of the parabola. A large positive value of a makes a narrow parabola; a positive value of a which is close to 0 makes the parabola wide. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value.

In either case, the vertex is a turning point on the graph. The graph is also symmetric with a vertical line drawn through the vertex, called the axis of symmetry. There is an easy way to tell whether the graph of a quadratic function opens upward or downward: if the leading coefficient is greater than zero, the parabola opens upward, and if the leading coefficient is less than zero, the parabola opens downward.

Vertical parabolas give an important piece of information: When the parabola opens up, the vertex is the lowest point on the graph — called the minimum, or min. If the solutions are real, but irrational radicals then we need to approximate their values and plot them.

The y -intercept of any graph is a point on the y -axis and therefore has x -coordinate 0. We can use this fact to find the y -intercepts by simply plugging 0 for x in the original equation and simplifying. Because this parabola opens upward, the axis of symmetry is the vertical line that intersects the parabola at the vertex. This parabola does not cross the x -axis, so it has no zeros. It crosses the y -axis at 0, 7 so this is the y -intercept. Skip to main content.

Quadratic Functions. Search for:. Because the vertex appears in the standard form of the quadratic function, this form is also known as the vertex form of a quadratic function. If we are given the general form of a quadratic function:. Rewrite the quadratic in standard form vertex form. Any number can be the input value of a quadratic function. Therefore the domain of any quadratic function is all real numbers. Because parabolas have a maximum or a minimum at the vertex, the range is restricted.

We need to determine the maximum value. The domain is all real numbers.