\(\text{y} = 3\text{x}\)

\(\text{y} = 2\text{x}^{2}\)

\(\text{y} = -3\text{x}^{2}\)

\(\text{y} = -6\text{x}\)

\(5\text{x} + \text{y} = 7\)

\(7\text{x}^{2} + \text{y} = 24\)

Persevere with Problems The graphs of quadratic functions may have exactly one highest point, called a maximum, or exactly one lowest point, called a minimum. Graph each quadratic equation. Determine whether each graph has a maximum or a minimum. If so, give the coordinates of each point.

a. \(\text{y} = 2\text{x}^{2} + 1\)

b. \(\text{y} = -\text{x}^{2} + 5\)

c. \(\text{y} = \text{x}^{2} - 3\)

Model with Mathematics Write the equation of a quadratic function that opens upward and has its minimum at (0, -3.5).

Reason Inductively The equation \(\text{y} = \text{a}\text{x}^{2} + \text{bx} + \text{c}\) represents a quadratic function. What does the constant c represent? Explain.