How do you find the axis of symmetry, and the maximum or minimum value of the function y = –3(x + 7)^2 – 10?

1 Answer
Mar 2, 2017

color(purple)("Thus the vertex is a maximum")
color(purple)("Vertex"->(x,y)=(-7,-10))
color(purple)("Axis of symmetry "->x=-7)

Explanation:

This is the vertex form of equation type y=ax^2+bx+c

If you were to square the brackets and multiply by the -3 the x^2 term would be -3x^2. As this is negative the graph is of general shape nn. color(purple)("Thus the vertex is a maximum")
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The coordinates of the vertex can be read directly from the given equation but you will need to 'tweak' it a bit.

Given: y=-3(xcolor(red)(+7))^2color(green)(-10)

x_("vertex")=(-1)xxcolor(red)(+7) =-7

y_("vertex")=color(green)(-10)

color(purple)("Vertex"->(x,y)=(-7,-10))
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The axis of symmetry passes through the vertex and is parallel to the x-axis (for a quadratic in x as is this one)

color(purple)("Axis of symmetry "->x=-7)

Tony BTony B