The axis of symmetry is \(x = \frac, 0\right)\) and (−3, 0), and the y-intercept is (0, −3) Solve Quadratic Equations Where a, b, and c are real numbers and a ≠ 0. The general form of a quadratic function is Quadratic Function and the Characteristics of the Graph The y-intercept is where the graph intersects the y-axis. The zeros are the x-intercepts where the graph intersects the x-axis. The axis of symmetry is the vertical line through the vertex and is x = −2. The vertex is the turning points and lowest point on the graph. If they exist, the x-intercepts represent the zeros, or roots, of the quadratic function, which are the values of x when y = 0.Įxample 1: Identify the Characteristics of a Parabolaĭetermine the vertex, axis of symmetry, zeros, and y-intercept of the parabola shown in figure 3. The x-intercepts are the points at which the parabola crosses the x-axis. The y-intercept is the point at which the parabola crosses the y-axis. The graph is also symmetric with a vertical line drawn through the vertex, called the axis of symmetry. In either case, the vertex is a turning point on the graph. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function.
An important feature of a parabola is its extreme point, called the vertex. The graph of a quadratic function is a U-shaped curve called a parabola. The graph of a quadratic function is called a parabola. They can be written as f( x) = ax 2 + bx + c. This is called projectile motion and can be modeled by a quadratic function.Ī quadratic function is a simple polynomial function where the highest exponent on x is 2. Then only gravity influences the water's motion until it hits the pool on the other side. The water in a fountain follows a curved path. Solve problems involving a quadratic function’s minimum or maximum value.įigure 1: Water fountain in Navy Pier in Chicago.Determine a quadratic function’s minimum or maximum value.Understand how the graph of a parabola is related to its quadratic function.Recognize characteristics of parabolas.
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