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quadratic function with (-2,4) as the vertex and passes through (-4,-4)

Sagot :

-2x^2 + 8 because if you turn it into vertex form and determine
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Answer:

[tex]f(x)=-2x^2-8x-4[/tex]

Step-by-step explanation:

Vertex form of quadratic function:  [tex]f(x)=a(x-h)^2+k[/tex]

where [tex](h,k)[/tex] is the vertex

Given:

  • vertex = (-2, 4)

[tex]\implies f(x)=a(x+2)^2+4[/tex]

Given:

  • point on curve = (-4, -4)

[tex]\implies f(-4)=-4\\\\\implies a(-4+2)^2+4=-4\\\\\implies a(-2)^2=-4-4\\\\\implies 4a=-8\\\\\implies a = -2[/tex]

Therefore,

[tex]f(x)=-2(x+2)^2+4\\\\\implies f(x)=-2(x^2+4x+4)+4\\\\\implies f(x)=-2x^2-8x-8+4\\\\\implies f(x)=-2x^2-8x-4[/tex]

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