Question

chen predicted that the function $f(x)=1.5x^2 - 9x + 7$ would have an axis of symmetry at $x = 3$ with the vertex at $(3,7)$. is chen correct? explain.
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. chen is correct.

b. chen is incorrect. he computed the x - coordinate incorrectly, so both coordinates of the vertex he found were wrong. the vertex is actually
(type an ordered pair, using integers or decimals.)

c. chen is incorrect. he identified the y - intercept as the y - coordinate of the vertex, but did not find the x - intercept correctly to find the x - coordinate of the vertex. the v
(type an ordered pair, using integers or decimals.)

d. chen is incorrect. he used the y - intercept as the y - coordinate of the vertex instead of evaluating the function at the x - coordinate of the vertex. the vertex is actually
(type an ordered pair, using integers or decimals.)

Explanation:

Step1: Find axis of symmetry

For quadratic $f(x)=ax^2+bx+c$, axis of symmetry is $x=-\frac{b}{2a}$.
Here $a=1.5$, $b=-9$, so:
$$x=-\frac{-9}{2\times1.5}=\frac{9}{3}=3$$

Step2: Calculate vertex y-coordinate

Substitute $x=3$ into $f(x)$:
$$f(3)=1.5(3)^2 -9(3)+7=1.5\times9 -27 +7=13.5-27+7=-6.5$$

Step3: Evaluate Chen's claim

Chen's x-coordinate for vertex is correct, but he used the y-intercept ($7$) instead of calculating $f(3)$. So the actual vertex is $(3, -6.5)$.

Answer:

D. Chen is incorrect. He used the y-intercept as the y-coordinate of the vertex instead of evaluating the function at the x-coordinate of the vertex. The vertex is actually (3, -6.5)