The equation of the quadratic function in standard form as required in the task content is; f(x) = -x² + 12x - 43.
<h3>Standard form equation of a quadratic function.</h3>
It follows from the task content that the standard form equation of the quadratic function is to.be determined.
Since the standard form equation can be derived from the vertex form equation as follows;
f(x) = a (x - h)² + k
f(x) = a (x - 6)² - 7
Hence, to find the value of a, Substitute x = 8 and f(x) = -11 so that we have;
-11 = a (8 - 6)² - 7
-11 = 4a - 7
4a = -4
a = -1.
Hence, the equation in vertex form is; f(x) = -1 (x -6)² - 7 and when expressed in standard form we have;
f(x) = -1(x² - 12x + 36) - 7
f(x) = -x² + 12x - 43
Therefore, the required equation in standard form is; f(x) = -x² + 12x - 43.
Read more on quadratic functions;
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Answer:
C)
Step-by-step explanation:
Note that one of the lines is simply y=-1 for any x, so we can dismiss the only answer without y=-1. That rejected answer is A)
Now let's notice, that the other line is decreasing y when increasing x. That tells us that in the equation y = ax + b, a has to be negative. This brings us to reject option D).
What is the y of that line for x = 0? Because y = ax + b, for x = 0 we will get the value of b. This is called the intercept. The line is at y=4 for x=0, so we know that the b in the equation must be positive 4. This fits answer C, but rejects answer B). And so, we have found that C) is the only possible answer.
Answer:
5
Step-by-step explanation:
You must have x alone
Answer:
Pythagorean theorem, eh?
Step-by-step explanation:
The way to do this is use the radius-tangent angle theorem thing...
It states that, a radius that intersects a point of tangency(I think that's what it's called) is perpendicular to the tangent. Thus, CW is perpendicular to OW!
Thus, it forms a right triangle, where we can use Pythagorean Theorem!
If you don't know what it is, check the internet! It's pretty simple.

So, there you go! Hope this helps!
NOTE: This answer was recently deleted for violating community guidelines, so I just re-uploaded it!(and edited it) So if you do need more help, do some research!
Answer:

Step-by-step explanation:
One is given the following equation;

The problem asks one to find the roots of the equation. The roots of a quadratic equation are the (x-coordinate) of the points where the graph of the equation intersects the x-axis. In essence, the zeros of the equation, these values can be found using the quadratic formula. In order to do this, one has to ensure that one side of the equation is solved for (0) and in standard form. This can be done with inverse operations;


This equation is now in standard form. The standard form of a quadratic equation complies with the following format;

The quadratic formula uses the coefficients of the quadratic equation to find the zeros this equation is as follows,

Substitute the coefficients of the given equation in and solve for the roots;

Simplify,

Therefore, the following statement can be made;
