What is the equation of the parabola that opens upwards with vertex at the origi
Practice Questions
Q1
What is the equation of the parabola that opens upwards with vertex at the origin and passes through the point (2, 8)?
y = 2x^2
y = x^2
y = 4x^2
y = 8x^2
Questions & Step-by-Step Solutions
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.
