Find the coordinates of the vertex and the equation of the axis of symmetry for the parabola with the given equation.y = x2 - 7x + 12
vertex= ?
axis line of symmetry equation?
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Answer:

The vertex is at ( 3.5, -0.25)

and the axis of symmetry is x = 3.5.

Step-by-step explanation:

Convert to vertex form:

y = x^2 - 7x + 12

y = (x - 3.5)^2 - 3.5^2 + 12

y = (x - 3.5)^2 - 0.25

y = (x - 3.5)^2 - 0.25.

So the vertex is at ( 3.5, -0.25)

and

the axis of symmetry is x = 3.5.

Final answer:

The vertex of the parabola y = x² - 7x + 12 is at (3.5,-0.25) and the equation of the axis of symmetry is x = 3.5.

Explanation:

The given quadratic equation is y = x² - 7x + 12. To determine the vertex and the equation of the axis of symmetry, we need to first find the x-coordinate of the vertex, which is determined by the formula -b/2a. Here in our equation, a = 1 (coefficient of x²) and b = -7 (coefficient of x), so x = -(-7)/(2*1) = 3.5.

The x-coordinate of the vertex is thus 3.5. Now, to get the y-coordinate of the vertex, we substitute x = 3.5 into our equation, so y = (3.5)² - 7*(3.5) + 12 = -0.25. Therefore, the vertex of the parabola is at (3.5,-0.25). The line of symmetry of a parabola always passes through the vertex, so the equation of the axis of symmetry is x = 3.5.

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