Hi Alena
When we're giving a problem like 5x^2-18x+52=0, we may be asked to solve equation or we may be asked to find the _____ intercepts or we may be asked to find the _____ or the ______.
You have a lot of blanks above, when asked to fill in data based on a Standard Form Quadratic, a parabola, set equal to zero, you can look up in your text and online the many features of the Standard Form Quadratic; for example
For
f(x) = ax2 + bx + c
0 = ax2 + bx + c
a is coefficient of x2 and determines which way your parabola opens
a>0 means your parabola opens upward
a<0 means your parabola opens downward
b is the coefficient of x and can be used with a to find the vertex of your parabola
the x coordinate of the vertex = -b/2a
Once this is determined you can plug the x value into your function to find the y coordinate of the vertex
c is a constant
For
0 = ax2 + bx + c
When x = 0, y = c, so (0, c) is your y intercept
0 = ax2 + bx + c
Can often be factored and if it cannot be factored one can use the Quadratic Formula to determine the x intercepts, sometime your parabola may not even cross the x axis but understanding the meaning of the variables and how they relate to the graph are usually easy to look up and read. Often knowing these will help to fill in many blanks.
For
5x2 - 18x + 52 =0
a = 5
b = -18
c = 52
I would suggest using the Quadratic Formula to find any x intercepts, there may be none
The y intercept can be found by setting x = 0 in this case the y intercept is (0, c) or (0,52)
a is positive so your parabola opens up
The x coordinate of the vertex is -(-18)/2(5) = 18/10 = 1.8 and so on
I hope this information helps
