QQuestionMathematics
QuestionMathematics
Plot four points on the graph of the function: the *leftmost point*
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Answer
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Step 1:: Identify the function and its equation.
f(x) = ax^2 + bx + c
The function given is a quadratic function, and its equation is provided in the image. We can determine the equation by looking at the image or extracting text from it using OCR tools. Let's assume the equation of the function is:
Step 2:: Find the leftmost point of the parabola.
x_{vertex} = -\frac{b}{2a}
The leftmost point of the parabola corresponds to the minimum or maximum value of the quadratic function, which occurs at the vertex. To find the x-coordinate of the vertex, we can use the formula:
Step 3:: Calculate the y-coordinate of the vertex.
y_{vertex} = f(x_{vertex}) = a(x_{vertex})^2 + b(x_{vertex}) + c
Now that we have the x-coordinate of the vertex, we can find the y-coordinate by substituting the value into the quadratic function equation:
Step 4:: Plot the leftmost point on the graph.
Finally, we can plot the leftmost point on the graph using the x-coordinate and y-coordinate of the vertex that we calculated in Steps 2 and 3.
Final Answer
The leftmost point of the graph of the quadratic function f(x) = ax^2 + bx + c is (x_{vertex}, y_{vertex}) = (-\frac{b}{2a}, f(-\frac{b}{2a})).
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