Instructions: Determine the shape and direction of the parabola formed by the given function.y=7x2𝑦=7𝑥2SolutionBecause a𝑎 is Answer 1 Question 8, the parabola opens Answer 2 Question 8.Because a𝑎 Answer 3 Question 8, the parabola is Answer 4 Question 8 about its line of symmetry which we call vertical Answer 5 Question 8.
Question
Instructions: Determine the shape and direction of the parabola formed by the given function.y=7x2𝑦=7𝑥2SolutionBecause a𝑎 is Answer 1 Question 8, the parabola opens Answer 2 Question 8.Because a𝑎 Answer 3 Question 8, the parabola is Answer 4 Question 8 about its line of symmetry which we call vertical Answer 5 Question 8.
Solution
The given function is y = 7x^2.
Step 1: Identify the coefficient of x^2. In this case, the coefficient is 7.
Step 2: Determine the direction of the parabola. If the coefficient of x^2 is positive, the parabola opens upwards. If it's negative, the parabola opens downwards. Here, since 7 is positive, the parabola opens upwards.
Step 3: Determine the shape of the parabola. The coefficient of x^2 determines the "narrowness" or "wideness" of the parabola. If the absolute value of the coefficient is greater than 1, the parabola is narrower than the standard parabola y = x^2. If it's less than 1, the parabola is wider. If it's equal to 1, the parabola has the standard shape. Here, since 7 is greater than 1, the parabola is narrower.
Step 4: Determine the line of symmetry. For a parabola in the form y = ax^2 + bx + c, the line of symmetry is x = -b/2a. Here, since there's no term bx, the line of symmetry is x = 0, which is the y-axis.
So, the parabola formed by the function y = 7x^2 opens upwards, is narrower than the standard parabola, and is symmetrical about the y-axis.
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