When “a” is positive, the graph of y = ax2 + bx + c opens upward and the vertex is the lowest point on the curve. As the value of the coefficient “a” gets larger, the parabola narrows. When “a” is negative, the parabola opens downward and the vertex is the highest point on the curve.

## What is the maximum point of a quadratic graph?

One important feature of the parabola is that it has an extreme point, called the vertex. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value.

## How does a affect the graph?

1. Changing the value of “a” changes the width of the opening of the parabola and that the sign of “a” determines whether the parabola opens upwards or downwards. 2. Changing the value of “b” will move the axis of symmetry of the parabola from side to side; increasing b will move the axis in the opposite direction.

## What is linear and quadratic functions?

What is the difference between linear and quadratic functions? A linear function is one of the form y = mx + c. The graph of these functions is a single straight line. A quadratic function is one of the form y = ax2 + bx + c. For each output for y, there can be up to two associated input values of x.

## Is a straight line a parabola?

Definition. A parabola is a curve where any point is at an equal distance from: a fixed point (the focus ), and. a fixed straight line (the directrix )

## Do all linear quadratic systems result in a solution?

A linear and quadratic system can be represented by a line and a parabola in the x y xy xy -plane. A line and a parabola can intersect zero, one, or two times, which means a linear and quadratic system can have zero, one, or two solutions.

## How do you tell if a function is quadratic from a graph?

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.