In Exercises 5–8, the graph of a quadratic function is given. Wri...

Question

In Exercises 5–8, the graph of a quadratic function is given. Write the function's equation, selecting from the following options.

Accepted Answer

Find out the equation of the quadratic function using the given graph. If you notice here, we have a graph with two points native 3 18 and 09. So we can use our points in our general form of function to determine our equation. So the general form F of X will be equals to A X minus H squared plus K where H K is the vertex of our pre. Now we also know a will be negative because our para is pointing downwards. We'll leave A for now and substitute in our vertex X minus -3, 4 x coordinate. That is all squared plus R K which is 18. We can now simplify A X plus three squared plus 18. Now, we need to find a to find this, we can make use of our Y intercept. A wire set is 09. We can set our entire thing equals to nine and replace our X with zero. This will allow us to solve for A, we get nine is equals to a multiplied by three squared plus 18 that equals to nine A plus 18, subtract 18 from both sides to get negative nine S equals to nine A or A is negative one. We can then substitute this back into all quiz F of X is equals sative X plus three squared plus 18. We can now expand our X plus three squared. It's native X square plus six X plus nine plus 18 to show they are negative to get negative X squared minus six X minus nine plus 18, which finally gives us negative X squared minus six X plus. Not now, we can't simplify this any further. So the answer to our problem turns out to be answer A OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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In Exercises 5–8, the graph of a quadratic function is given. Write the function's equation, selecting from the following options.

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