Question

Create the graph for the quadratic function y=2x2−4.5x+2
to find the coordinates of the vertex of the parabola.(1 point)
Responses

(1.125,−2.5)
left parenthesis 1.125 comma negative 2.5 right parenthesis

(−0.53,1.13)
left parenthesis negative 0.53 comma 1.13 right parenthesis

(1.125,−0.531)
left parenthesis 1.125 comma negative 0.531 right parenthesis

(−1.125,4.531)

Answer 1

To find the vertex of the quadratic function \(y = 2x^2 - 4.5x + 2\), we can use the vertex formula for a quadratic equation in the form \(y = ax^2 + bx + c\). The x-coordinate of the vertex is given by:

\[
x = -\frac{b}{2a}
\]

Here, \(a = 2\) and \(b = -4.5\).

Calculating the x-coordinate of the vertex:

\[
x = -\frac{-4.5}{2 \cdot 2} = \frac{4.5}{4} = 1.125
\]

Now, substituting \(x = 1.125\) back into the original equation to find the y-coordinate:

\[
y = 2(1.125)^2 - 4.5(1.125) + 2
\]

Calculating \(2(1.125)^2\):

\[
2(1.125)^2 = 2 \cdot 1.265625 = 2.53125
\]

Calculating \(-4.5(1.125)\):

\[
-4.5(1.125) = -5.0625
\]

Now substituting these values into the equation:

\[
y = 2.53125 - 5.0625 + 2 = -0.53125
\]

Thus, the coordinates of the vertex are:

\[
(1.125, -0.53125)
\]

Rounding this to three decimal places gives us the vertex as:

\[
(1.125, -0.531)
\]

Therefore, the correct response is:

\[
\text{(1.125,−0.531)}
\]