What is the equation of the parabola that opens upwards with vertex at the origi

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Question: What is the equation of the parabola that opens upwards with vertex at the origin and passes through the point (2, 8)?

Options:

Correct Answer: y = 4x^2

Solution:

The vertex form of a parabola is y = ax^2. Since it passes through (2, 8), we have 8 = a(2^2) => 8 = 4a => a = 2. Thus, the equation is y = 4x^2.

What is the equation of the parabola that opens upwards with vertex at the origin and passes through the point (2, 8)?

What is the equation of the parabola that opens upwards with vertex at the origin and passes through the point (2, 8)?

Step 1: Understand that the equation of a parabola that opens upwards with its vertex at the origin (0, 0) is in the form y = ax^2, where 'a' is a constant.
Step 2: Identify the point that the parabola passes through, which is (2, 8). This means when x = 2, y = 8.
Step 3: Substitute the point (2, 8) into the equation y = ax^2. This gives us 8 = a(2^2).
Step 4: Calculate 2^2, which is 4. So now we have 8 = 4a.
Step 5: To find 'a', divide both sides of the equation by 4. This gives us a = 8 / 4.
Step 6: Simplify 8 / 4 to get a = 2.
Step 7: Now that we have 'a', substitute it back into the equation y = ax^2. This gives us y = 2x^2.
Step 8: Therefore, the final equation of the parabola is y = 2x^2.

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