Solving Quadratic & Graph of y= |x+a| +b

In summary, F(x) = -x² -6x -7 has a maximum value and can be found by completing the square. For #2, the values of a and b affect the graph by shifting it along the x-axis and vertically.
  • #1
Chikawakajones
22
0
2 Problems.!

#1 Tell Whether The Quadratic Has A Maximum Value Or A Minimum Value. The Find The Value. Round To The Nearest Tenth.

F(x)= -x² -6x - 7


#2 Let y = | x+a | +b, Where a ‡ 0 and b ‡ 0 . Explain how the values of a and b affect the graph of the functions as compared to the graph of y= |x|.



I NEED HELP FAST HURRY! THANK YOU!
 
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  • #2
QUICK! Tell us what you did so far so we can HELP YOU! :-)
 
  • #3
Chikawakajones said:
#1 Tell Whether The Quadratic Has A Maximum Value Or A Minimum Value. The Find The Value. Round To The Nearest Tenth.

F(x)= -x² -6x - 7

F has a max. I'm not sure how to do it without calculus though. i guess there's something about the coefficients of F...


#2 Let y = | x+a | +b, Where a ‡ 0 and b ‡ 0 . Explain how the values of a and b affect the graph of the functions as compared to the graph of y= |x|.
the a moves the graph along the x-axis, the b loves it up & down. how? how about you figure it out... :wink:
 
  • #4
You can complete the square to find the max.
 

FAQ: Solving Quadratic & Graph of y= |x+a| +b

How do I solve a quadratic equation?

To solve a quadratic equation, you can use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. Alternatively, you can factor the equation and solve for the roots.

What is the vertex form of a quadratic equation?

The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola.

How do I graph a quadratic equation?

To graph a quadratic equation, you can plot points by substituting different values of x into the equation and then connecting them with a smooth curve. Alternatively, you can use the vertex form to determine the vertex and plot the parabola from there.

What is the effect of a and b in the equation y = |x+a| + b?

The value of a affects the slope of the graph and the value of b affects the y-intercept. The absolute value function ensures that the graph is always above the x-axis.

Can a quadratic equation have more than two solutions?

No, a quadratic equation can have at most two solutions. This is because the graph of a quadratic equation is a parabola, which can intersect the x-axis at most twice.

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