Question

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Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point. (Let x be the independent variable and y be the dependent variable.)

Answer 1

`y=3x^2-6x-2`

Explanation:

`\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}`

Given:

• Vertex = (1, -5)
• Point = (-1, 7)

Substitute the given vertex and point into the vertex formula and solve for a:

`\implies 7=a(-1-1)^2-5`

`\implies 7=a(-2)^2-5`

`\implies 7=4a-5`

`\implies 12=4a`

`\implies a=3`

Substitute the found value of a together with the vertex into the formula and expand to standard form:

`\implies y=3(x-1)^2-5`

`\implies y=3(x-1)(x-1)-5`

`\implies y=3(x^2-2x+1)-5`

`\implies y=3x^2-6x+3-5`

`\implies y=3x^2-6x-2`