Express $y=2{{x}^{2}}+4x-6$ in the form $a{{(x+b)}^{2}}+k$, where $a$, $b$ and $k$ are constants. State the minimum value of the function and the value of $x$ when this occurs. Hence, sketch the graph of $y=2{{x}^{2}}+4x-6$ and state the coordinates of $x$ and $y$-intercepts and turning points.

Quadratic Functions, Equations and Inequalities - Maximum and Minimum Values of General Quadratic Functions

IP 3

Express $y=2{{x}^{2}}+4x-6$ in the form $a{{(x+b)}^{2}}+k$, where $a$, $b$ and $k$ are constants.

State the minimum value of the function and the value of $x$ when this occurs.
Hence, sketch the graph of $y=2{{x}^{2}}+4x-6$ and state the coordinates of $x$ and $y$-intercepts and turning points.

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Answer:y = 2(x+1)^2 - 8; minimum -8 at x = -1; turning point (-1,-8); x-intercepts (-3,0),(1,0); y-intercept (0,-6).

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