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Use a graphing calculator to approximate the vertex of the graph of the parabola defined by the following equation.

[tex]\[ y = x^2 + 2x - 9 \][/tex]

A. [tex]\((-1, -10)\)[/tex]
B. [tex]\((-1, -9)\)[/tex]
C. [tex]\((1, 10)\)[/tex]
D. [tex]\((1, -10)\)[/tex]

Please select the best answer from the choices provided:
A, B, C, or D.



Answer :

GinnyAnswer
To find the vertex of a parabola given by the equation [tex]\( y = x^2 + 2x - 9 \)[/tex], we can use the vertex formula.

The general form of a quadratic equation is [tex]\( y = ax^2 + bx + c \)[/tex]. For this specific equation:
- [tex]\( a = 1 \)[/tex]
- [tex]\( b = 2 \)[/tex]
- [tex]\( c = -9 \)[/tex]

The x-coordinate of the vertex can be found using the formula:
[tex]\[ x = -\frac{b}{2a} \][/tex]

Substituting the given values:
[tex]\[ x = -\frac{2}{2 \cdot 1} = -1 \][/tex]

Now that we have the x-coordinate, we can find the y-coordinate by substituting [tex]\( x = -1 \)[/tex] back into the original equation:
[tex]\[ y = (-1)^2 + 2(-1) - 9 \][/tex]
[tex]\[ y = 1 - 2 - 9 \][/tex]
[tex]\[ y = -10 \][/tex]

Therefore, the vertex of the parabola is [tex]\( (-1, -10) \)[/tex].

From the given choices, the correct answer is:
[tex]\[ \boxed{A} \][/tex]

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