Question

in the quadratic regression screen shown in the problem statement, why is the value of the coefficient a negative?
a. since the height increases then decreases, the quadratic graph must open upward, not downward, which means a must be negative
b. the height decreases then increases, which looks like a quadratic function
c. the height increases then decreases, which looks like a quadratic function
d. the height starts decreasing more and more rapidly, which looks like a quadratic function
b. use the graphing calculator screen (shown in the box above) to express the model in function notation.
f(x) = -0.9x² + 2.7x + 6.7
c. use the model from part (b) to determine the x - coordinate of the quadratic functions vertex
the x - coordinate of the vertex is □.
(type an integer or a decimal rounded to one decimal place as needed.)

Explanation:

Step1: Recall the formula for the x - coordinate of the vertex of a quadratic function

For a quadratic function \(y = ax^{2}+bx + c\), the formula for the x - coordinate of the vertex is \(x=-\frac{b}{2a}\).

Step2: Identify the values of \(a\) and \(b\) from the given function

Given the function \(f(x)=-0.9x^{2}+2.7x + 6.7\), we have \(a=-0.9\) and \(b = 2.7\).

Step3: Substitute the values of \(a\) and \(b\) into the vertex formula

$$
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$$

Answer:

\(1.5\)