To find the y-intercept of the quadratic function \( y = x^2 + 2x + 4 \), we need to evaluate the function at \( x = 0 \):
\[ y = (0)^2 + 2(0) + 4 \] \[ y = 0 + 0 + 4 \] \[ y = 4 \]
Thus, the y-value of the y-intercept is 4.
To graph the quadratic function, you would plot the y-intercept at the point (0, 4) and then determine other points by substituting different x-values into the equation. The vertex of the parabola can also be found using the vertex formula. The x-coordinate of the vertex for a quadratic in the form \( ax^2 + bx + c \) is given by \( x = -\frac{b}{2a} \).
In this case, \( a = 1 \) and \( b = 2 \):
\[ x = -\frac{2}{2(1)} = -1 \]
Now substitute \( x = -1 \) back into the equation to get the y-coordinate of the vertex:
\[ y = (-1)^2 + 2(-1) + 4 \] \[ y = 1 - 2 + 4 \] \[ y = 3 \]
So the vertex of the parabola is at the point (-1, 3).
You can sketch the parabola using the vertex and the y-intercept along with other calculated points for a complete graph.
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