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).

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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).       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

Select all the true statements for the quadratic function
f%28x%29+=+5x%5E2+%2B+70x+%2B+245
write in vertex form f%28x%29+=+a%28x-h%29%5E2+%2B+k+, where h and k are x+and y+coordinates of vertex
complete square
f%28x%29+=+5%28x%5E2+%2B+14x%29+%2B+245
f%28x%29+=+5%28x%5E2+%2B+14x%2Bb%5E2%29-5b%5E2+%2B+245......b=14%2F2=7
f%28x%29+=+5%28x%5E2+%2B+14x%2B7%5E2%29-5%2A7%5E2+%2B+245
f%28x%29+=+5%28x+%2B7%29%5E2-245+%2B+245
f%28x%29+=+5%28x+%2B7%29%5E2
=> h=-7, k=0
answer: all the true statements are
B. The vertex of the function is at (-7, 0).=>true
D. The function is decreasing when -infinity+%3C+x+%3C+-7.=>true
E. The range of the function is all positive real numbers including zero.=>true

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+5%28x+%2B7%29%5E2%29+


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


The function is 5x%5E2%2B70x%2B245 = 5%28x%5E2%2B14x%2B49%29 = 5%28x%2B7%29%5E2

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) About Me  (Show Source):
You can put this solution on YOUR website!
graph%28400%2C400%2C-11%2C-1%2C-2%2C12%2C5x%5E2%2B70x%2B245%29

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

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