SOLUTION: A quadratic function is given by y=5x^2+7+11. For what domain values of y, the solution of x will be a real number?

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Question 1047672: A quadratic function is given by y=5x^2+7+11. For what domain values of y, the solution of x will be a real number?
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
All real numbers for x will give a RANGE of real numbers for y. The equation has a restriction for its RANGE. Range is all values greater than the y-coordinate of the vertex.

y=5%28x%5E2%2B%287%2F5%29x%2B11%2F5%29

5%28x%5E2%2B%287%2F5%29x%2B%287%2F10%29%5E2%2B11%2F5-%287%2F10%29%5E2%29

5%28%28x%2B7%2F10%29%5E2%2B11%2F5-%287%2F10%29%5E2%29

5%28%28x%2B7%2F10%29%5E2%2B220%2F100-49%2F100%29

5%28%28x%2B7%2F10%29%5E2%2B171%2F100%29

y=5%28x%2B7%2F10%29%5E2%2B171%2F20, Square completed, now in standard form.
The range is all real numbers greater than or equal to 171%2F20.