Which parabola will have one real solution with the line y = x - 5?
y = x² + x - 4
y = x² + 2x - 1
y = x² + 6x + 9
y = x² + 7x + 4 

Solution:

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line.

The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.

Given, line y = x - 5

y = x - 5 --- (1)

Consider the equation y = x² + 7x + 4 --- (2)

By equating both

x - 5 = x² + 7x + 4

x² + 6x + 9 = 0

Here

b² - 4ac = 6² + 6(1) + 9

= 36 - 36 = 0

The system has one real solution.

Therefore, x² + 7x + 4 has one real solution.

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Which parabola will have one real solution with the line y = x - 5?

Summary:

Parabola that has one real solution with the line y = x - 5 is x² + 7x + 4.