Find the vertex F(x)=5x²-10x+3
1 answer:
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<h2>Exponential Functions</h2>
Exponential functions are typically organized in this format:
To find the equation given the graph of an exponential function:
- Identify the horizontal asymptote
⇒ <em>asymptote</em> - a line towards which a graph appears to travel but never meets
⇒ If the horizontal asymptote is not equal to 0, we add this at the end of the function equation. - Identify the y-intercept
⇒ This is our <em>a</em> value. - Identify a point on the graph and solve for <em>c</em>
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<h2>Solving the Question</h2>Identify the horizontal asymptote
In this question, it appears to be x = 0.
Identify the y-intercept
The y-intercept is the value of <em>y</em> at which the graph appears to cross the y-axis. In this graph, it appears to be 100. This is our <em>a</em> value. Plug this into :
Solve for <em>c</em>
We can use any point that falls on the graph for this step. For instance, (1,50) appears to be a valid point. Plug this into our equation and solve for <em>c</em>:
Plug <em>c</em> back into our original equation:
Answer:
x =
Step-by-step explanation:
Using Pythagorean Theorem we can say;
15² + x² = 18²
225 + x² = 324
x² = 99
x =
To simplify this in the radical for we can say:
So the answer =
Hope this helps!