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

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

(−1.125,4.531)
left parenthesis negative 1.125 comma 4.531 right parenthesis

(−0.53,1.13)

Answer 1

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

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

In this case, \( a = 2 \) and \( b = -4.5 \). Plugging in the values:

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

Next, we substitute \( x = 1.125 \) back into the original equation to find the \(y\)-coordinate of the vertex:

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

Calculating \( (1.125)^2 \):

\[
(1.125)^2 = 1.265625
\]

Now substituting into \(y\):

\[
y = 2(1.265625) - 4.5(1.125) + 2
\]

Calculating \( 2(1.265625) \):

\[
2(1.265625) = 2.53125
\]

Calculating \( -4.5(1.125) \):

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

Putting it all together:

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

Therefore, the coordinates of the vertex of the parabola are:

\[
(1.125, -0.53125)
\]

This is closest to the response \( (1.125, -0.531) \).

The correct answer is:

**(1.125, -0.531)**