Match the given quadratic function y=ax²+bx+c to its equivalent standard form y=a(x-h)²+k
Answer (1)
Answer:Identify the coefficients: ( a ), ( b ), and ( c ) from the quadratic function ( y = ax^2 + bx + c ).Calculate ( h ): [ h = -\frac{b}{2a} ]Calculate ( k ): [ k = c - \frac{b^2}{4a} ]Rewrite the function: Substitute ( h ) and ( k ) back into the standard form equation.ExampleLet’s convert ( y = 2x^2 + 8x + 6 ) to the standard form.Identify coefficients: ( a = 2 ), ( b = 8 ), ( c = 6 ).Calculate ( h ): [ h = -\frac{8}{2 \cdot 2} = -2 ]Calculate ( k ): [ k = 6 - \frac{8^2}{4 \cdot 2} = 6 - 8 = -2 ]Rewrite the function: [ y = 2(x + 2)^2 - 2 ]So, the standard form of ( y = 2x^2 + 8x + 6 ) is ( y = 2(x + 2)^2 - 2 ).Step-by-step explanation:
