Answer:
y = x² -14x +24
Step-by-step explanation:
You want a quadratic with x-intercepts that differ by 10 and a y-intercept of 24.
Quadratic
If the roots are p and q, then we require ...
y = (x -p)(x -q) = x² -(p+q)x +pq
The y-intercept is pq, which the problem requires to be 24. Then p and q will be factors of 24 that differ by 10.
Factoring
The value 24 can be factored as ...
24 = 1·24 = 2·12 = 3·8 = 4·6
The factor differences are, in order, 23, 10, 5, 2. We want the factors that differ by 10, so we can choose ...
p = 2, q = 12
and the quadratic is ...
y = x² -(2 +12)x +24
y = x² -14x +24 . . . . . . desired quadratic
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Additional comment
Reflecting the curve across the y-axis will not change the y-intercept or the difference of the roots. That equation would be ...
y = x² +14x +24
