Based on the information provided, it is not possible to determine which picture matches the original parabola, x^2 - 5x + 9, as the pictures of the parabolas were not described or provided.
To find the number of x-intercepts, we can analyze the discriminant of the quadratic equation. The discriminant is given by
b^2 - 4ac
where a is the coefficient of x^2, b is the coefficient of x, and c is the constant term.
For the equation x^2 - 5x + 9, we have a = 1, b = -5, and c = 9.
The discriminant is calculated as (-5)^2 - 4(1)(9) = 25 - 36 = -11.
Since the discriminant is negative, we can conclude that the quadratic equation x^2 - 5x + 9 does not have any x-intercepts.
On the last slide, we ended up with an ERROR message when we tried to take sqrt(- 9) This happened because it is "impossible" to take the square root of a negative number. Think : 3 ^ 2 = 9 and (- 3) ^ 2 = 9 but it is impossible x ^ 2 = - 9 to find a number such that . Examine the picture of the 3 parabolas . Which picture do you think matches the original parabola , x ^ 2 - 5x + 9 ? How many x-intercepts will we see ? No x-intercept One x - intercept Two x-intercepts
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