The equation 2 x - 4 y = 7 is written in slope-intercept form. True False
1 answer:
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Answer:
1) x ≤ 2 or x ≥ 5
2) -6 < x < 2
Step-by-step explanation:
1) We have x^2 - 7x + 10, so let's factor this as if this were a regular equation:
x^2 - 7x + 10 = (x - 2)(x - 5)
So, we now have (x - 2)(x - 5) ≥ 0
Let's imagine this as a graph (see attachment). Notice that the only place that is above the number line is considered greater than 0, and that's when x ≤ 2 or x ≥ 5 (the shaded region).
2) Again, we have x^2 + 4x - 12, so factor this as if this were a regular equation:
x^2 + 4x - 12 = (x + 6)(x - 2)
So now we have (x + 6)(x - 2) < 0
Now imagine this as a graph again (see second attachment). Notice that the only place that is below 0 (< 0) is when -6 < x < 2 (the shaded region).
Hope this helps!
Answer:
C. The x-coordinate of the vertex must be 6
Step-by-step explanation:
The parabola intercepts the x-axis when y = 0.
Therefore, if the quadratic equation has the points (2, 0) and (10, 0) then the x-intercepts or "zeros" are x = 2 and x = 10.
The x-coordinate of the vertex is the midpoint of the zeros.
Therefore, the solution is option C.
<u>Additional Information</u>
The leading coefficient of a quadratic tells us if the parabola opens upwards or downwards:
- Positive leading coefficient = parabola opens upwards
- Negative leading coefficient = parabola opens downwards
We have not been given this information and so therefore cannot determine the way in which it opens.
As we do not know the way in which way the parabola opens, we cannot determine if the parabola will have a negative or positive y-intercept.
We have not been given the full quadratic equation, and so we cannot determine if the parabola is wider (or narrower) than the parent function.