1. How many real solutions does the function shown on the graph have?
The graph is following the function: y=(x+2)^2
A. No real solutions
B. One real solution** My answer
C. Two real solutions
D. Cannot be determined
2. What is the solution to 3x^2+3x+5=0?
I have the answers down to either -3(+or-)i squareroot51 / 6 or 3(+or-) i squareroot51 / 6
(I have to use the quadratic function)
Thank you so much!
I agree with #1
The way you typed the answer to #2 would indicate 4 answers, but a quadratic has only 2 solutions.
Be careful how you use the quadratic formula:
for ax^2 + bx + c = 0
x = (-b ± √(b^2 - 4ac) )/(2a)
in your case:
x = (-3 ± √-51)/6
= (-3 ± √51 i)/6 , and that's all
the ± only applied to the square root part.
Yes, sorry about that! I didn't know how to type in the necessary symbols. I was only confused concerning the 3 in the final answer. I wasn't sure if it was meant to be -3 or 3. From my understanding, I was right in thinking it was -3, right? :)
yes, look at my final answer
1. To determine the number of real solutions for the function y = (x+2)^2, we can look at the graph or use algebraic methods.
If we examine the graph of the function y = (x+2)^2, we can see that the parabola opens upwards and its vertex is at (-2, 0). Since the vertex is at the x-coordinate -2, the graph does not intersect the x-axis. Therefore, there are no real solutions to this function.
Alternatively, we can also use algebraic methods to determine the number of real solutions. The given function, y = (x+2)^2, is in vertex form. When a quadratic function is in vertex form, any value of x will result in a positive value of y since the squared term is always non-negative. Since y is always positive or zero, there are no values of x that will make y equal to zero, and therefore, there are no real solutions.
So, the correct answer is A. No real solutions.
2. To find the solutions to 3x^2 + 3x + 5 = 0, we can use the quadratic formula.
The quadratic formula states that for any quadratic equation in the form ax^2 + bx + c = 0, the solutions (also known as roots) can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the given equation, a = 3, b = 3, and c = 5. Plugging these values into the quadratic formula:
x = (-3 ± √(3^2 - 4(3)(5))) / (2(3))
x = (-3 ± √(9 - 60)) / 6
x = (-3 ± √(-51)) / 6
At this point, we encounter a negative under the square root (√), which means we have imaginary solutions, denoted by the imaginary unit "i." Therefore, the solutions to the equation 3x^2 + 3x + 5 = 0 are:
x = (-3 ± i√(51)) / 6
So, your answer options of -3 ± i√51 / 6 or 3 ± i√51 / 6 are correct.