Skip to content

Elementary Graphing Problems

Method of Graphing the Quadratics

For each problem, follow these steps:

  1. Identify the Function: Write down the quadratic function in the form \(f(x) = ax^2 + bx + c\).

  2. Determine Key Points:

  3. Vertex: Use the vertex formula \(x = -\frac{b}{2a}\) to find the x-coordinate of the vertex. Substitute this value back into the function to find the y-coordinate.

  4. Y-Intercept: Set \(x = 0\) and solve for \(f(0)\) to find the y-intercept.

  5. Plot Points: Plot the vertex and the y-intercept on the graph. Find additional points by substituting values of \(x\) into the function if needed.

  6. Find the Roots (x-intercepts):

  7. Graph the Function: Plot the quadratic function based on the points calculated and the shape of the parabola.

  8. Identify the x-Intercepts: The x-intercepts are where the graph crosses the x-axis (where \(f(x) = 0\)).

  9. Draw the Parabola: Sketch the curve of the parabola based on the plotted points and the vertex.

By graphing the quadratic functions and locating the x-intercepts, you can visually understand how quadratic equations can be solved using their graphical representations.

Use the demos graphing tool to explore the proeprties and attributes of quadratic funnctions.

Problem 1.

Problem Statement: Graph the quadratic function \(f(x) = x^2 - 4\) and find the roots of the equation \(x^2 - 4 = 0\).

Problem 2.

Problem Statement: Graph the quadratic function \(f(x) = x^2 + 2x - 3\) and determine the x-intercepts of the graph.

Problem 3.

Problem Statement: Graph the quadratic function \(f(x) = x^2 - 6x + 8\) and identify the points where the graph intersects the x-axis.

Problem 4.

Problem Statement: Graph the quadratic function \(f(x) = 2x^2 - 4x - 6\) and find the roots of the equation.

Problem 5.

Problem Statement: Graph the quadratic function \(f(x) = -x^2 + 2x + 3\) and determine the x-intercepts.

Problem 6.

Problem Statement: Graph the quadratic function \(f(x) = x^2 + 4x + 4\) and find where the graph intersects the x-axis.

Problem 7.

Problem Statement: Graph the quadratic function \(f(x) = 3x^2 - 12x + 9\) and identify the roots of the equation.

Problem 8.

Problem Statement: Graph the quadratic function \(f(x) = -2x^2 + 5x + 1\) and determine the points where the graph crosses the x-axis.

Problem 9.

Problem Statement: Graph the quadratic function \(f(x) = x^2 - 2x - 3\) and find the x-intercepts.

Problem 10.

Problem Statement: Graph the quadratic function \(f(x) = 4x^2 - 16x + 15\) and determine where the graph intersects the x-axis.

Problem 11.

Problem Statement: Graph the quadratic function \(f(x) = x^2 + 6x + 8\) and find the roots of the equation.

Problem 12.

Problem Statement: Graph the quadratic function \(f(x) = 5x^2 - 20x + 15\) and identify the points where the graph crosses the x-axis.