Question

Write the equation of the quadratic function (-2,5) in the graph in standard form. (2 points) Standard form of the quadratic is y= _x^2+ _x+_.

Answer 1

1 and 4 are negative, but 9 is incorrect and I couldn't figure out what the last one was.

Answer 2

To write the equation of a quadratic function in standard form, we typically use the vertex form, which is:

\[ y = a(x - h)^2 + k \]

where \((h, k)\) is the vertex of the parabola. In this case, the vertex given is \((-2, 5)\), so we have:

\[ y = a(x + 2)^2 + 5 \]

To convert this into standard form \(y = ax^2 + bx + c\), we need to expand it. To do this, we need a value for \(a\). If we assume \(a = 1\) as a starting point (since you didn't provide any additional points for the vertex), we would have:

1. Expanding the expression:
\[
y = 1(x + 2)^2 + 5
\]
\[
= 1(x^2 + 4x + 4) + 5
\]
\[
= x^2 + 4x + 4 + 5
\]
\[
= x^2 + 4x + 9
\]

So with \(a = 1\), the quadratic is:

\[ y = 1x^2 + 4x + 9 \]

If you have another point or specific value for \(a\), you can adjust accordingly.

Therefore, the equation in standard form, assuming \(a = 1\), is:

\[ y = 1x^2 + 4x + 9 \]

You can fill in the blanks as follows:

Standard form of the quadratic is \(y = 1x^2 + 4x + 9\).