Answer:
Step-by-step explanation:
Good idea to review quadratic functions and the quadratic formula.
Quadratics have three coefficients: ax² + bx + c, and the "discriminant" is defined as b²-4ac. Please review these rules:
1) if the discriminant is +, the quadratic equation has two real, unequal roots.
2) if the disc. is 0, the equation has two real, equal root.
3) If the disc. is - , the equation has two complex roots.
Here a = 1, b = -3 and c = 4. Therefore the discriminant is (-3)²-4(1)(4), or
-7. Rule 3) applies: the equation has two complex roots, but no real ones. Thus we know that the graph does not cross the x-axis.
Graphing the given quadratic, x² - 3x + 4, using a dashed "line," is helpful. As you can see in the illustration of this graph, the graph neither touches nor crosses the x-axis. Thus, y = x² - 3x + 4 is greater than 0 for all x. The answer: All real numbers.
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![\sqrt{[(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}]}](https://tex.z-dn.net/?f=%5Csqrt%7B%5B%28x_%7B2%7D-x_%7B1%7D%29%5E%7B2%7D%2B%28y_%7B2%7D-y_%7B1%7D%29%5E%7B2%7D%5D%7D%20)
![\sqrt{[(3-(-4))^{2}+(-1-(-5))^{2}]}](https://tex.z-dn.net/?f=%5Csqrt%7B%5B%283-%28-4%29%29%5E%7B2%7D%2B%28-1-%28-5%29%29%5E%7B2%7D%5D%7D%20)
![\sqrt{[7^{2}+4^{2}]}](https://tex.z-dn.net/?f=%5Csqrt%7B%5B7%5E%7B2%7D%2B4%5E%7B2%7D%5D%7D%20)
![\sqrt{[49+16]}](https://tex.z-dn.net/?f=%5Csqrt%7B%5B49%2B16%5D%7D%20)
