x²+5
the quadratic parent function shifted up 5
To work with a quadratic expression of the form x²+5.
1. To simplify or factor this expression, you can’t do much because it is already in its simplest form. You can verify this by attempting to factor it using the formula a²+b²=(a+b)(a-b), which will not work for x²+5 because it is not a sum of squares.
2. To solve the equation x²+5=0, you can use the square root property. Subtracting 5 from both sides, we get x²=-5. Taking the square root of both sides, we get x=±√(-5), which is not a real number. Therefore, the equation x²+5=0 has no real solutions.
3. To graph this quadratic expression, you can plot points on a coordinate plane or use software. The graph of x²+5 is a parabola that opens upwards and has its vertex at (0, 5), (since x=0 corresponds to the minimum value of y=5). The parabola does not intersect the x-axis, indicating that there are no real roots, as we saw in part 2.
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