# Question Video: Using the Vertex Form of a Quadratic Function Mathematics • 9th Grade

Determine the quadratic function π with the following properties: Its graph has a vertex at (3, β17). π(4) = 5.

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### Video Transcript

Determine the quadratic function π with the following properties. Its graph has a vertex at three, negative 17. And π of four equals five.

Weβve been given a vertex and a solution point, which means we should think about the vertex form of quadratic functions. Which is π of π₯ equals π times π₯ minus β squared plus π, where β, π is the vertex, and π is some constant value. Using this form π of π₯ equals π times π₯ minus β squared plus π, we can plug in three for β and negative 17 for π. Which gives us π of π₯ equals π times π₯ minus three squared plus negative 17. Plus negative 17 can be simplified to, say, minus 17.

But in order to find π, weβll need to use the point we were given. If π of four equals five, then we plug in four for π₯ and five for π of π₯. Four minus three is one. One squared is one. π times one equals π. So, we have five equals π minus 17. And if we add 17 to both sides, we see that π equals 22. And so, we can go back to our original equation and plug in 22 for π. And we get the equation π of π₯ equals 22 times π₯ minus three squared minus 17.