SOLUTION: Select all the true statements for the quadratic function f(x) = 5x² + 70x + 245. Ⓐ The y-intercept of the function is −7. Ⓑ The vertex of the function is at (−7, 0).

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Question 1205875: Select all the true statements for the quadratic function
f(x) = 5x² + 70x + 245.
Ⓐ The y-intercept of the function is −7.
Ⓑ The vertex of the function is at (−7, 0).
Ⓒ The function is symmetric about the line x = 7.
Ⓓ The function is decreasing when −∞ < x < −7.
Ⓔ The range of the function is all positive real numbers including zero.

Found 3 solutions by MathLover1, greenestamps, josgarithmetic:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

Select all the true statements for the quadratic function

write in vertex form , where and are and coordinates of vertex
complete square

......



=> ,
answer: all the true statements are
B. The vertex of the function is at (, ).=>
D. The function is decreasing when .=>
E. The range of the function is all positive real numbers including zero.=>




Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


The function is = =

That is a parabola with vertex at (-7,0) and opening upward.

Ⓐ The y-intercept of the function is −7.
FALSE. The y-intercept (when x=0) is (0,245), or just 245. -7 (or (-7,0)) is the x-intercept, not the y-intercept.

Ⓑ The vertex of the function is at (−7, 0).
TRUE

Ⓒ The function is symmetric about the line x = 7.
FALSE. It is symmetric about the line x = -7.

Ⓓ The function is decreasing when −∞ < x < −7.
TRUE. And increasing when -7 < x < ∞.

Ⓔ The range of the function is all positive real numbers including zero.
I'm not sure how to answer this one. "all positive real numbers including zero" is self-contradictory....


Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!


Ⓔ The range of the function is all positive real numbers including zero.

Almost! That needs to say, "all positive real numbers AND zero".

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