<\/span><\/h2>\nTo find the minimum or maximum value of a parabola, you can follow these steps:<\/p>\n
Step 1:<\/b> Ensure the quadratic equation is in standard form, i.e., y = ax^2 + bx + c.<\/p>\n
Step 2:<\/b> Identify the values of the coefficients a, b, and c.<\/p>\n
Step 3:<\/b> Calculate the x-coordinate of the vertex using the formula:
\nx = -b \/ (2a). This formula gives you the symmetry axis of the parabola.<\/p>\n
Step 4:<\/b> Substitute the x-coordinate from step 3 into the original equation to find the corresponding y-coordinate of the vertex.<\/p>\n
Step 5:<\/b> The minimum or maximum value of the parabola is given by the y-coordinate obtained in step 4.<\/p>\n
Example:<\/b> Let’s consider the parabolic equation y = 2x^2 + 4x + 1 to illustrate these steps.<\/p>\n
Step 1:<\/b> The equation y = 2x^2 + 4x + 1 is already in standard form.<\/p>\n
Step 2:<\/b> The coefficients are a = 2, b = 4, and c = 1.<\/p>\n
Step 3:<\/b> Calculate the x-coordinate of the vertex:
\nx = -4 \/ (2 * 2) = -1.<\/p>\n
Step 4:<\/b> Substitute x = -1 into the equation:
\ny = 2(-1)^2 + 4(-1) + 1 = -1.<\/p>\n
Step 5:<\/b> The minimum or maximum value is y = -1.<\/p>\n
…and that’s it!<\/b> You have successfully found the minimum or maximum value of the parabola.<\/p>\n