Question

What is the general form of the quadratic with vertex at (2, 3) and passing through the point (5, 12)?

Answer 1

The general form of the quadratic with vertex at (2, 3) and passing through the point (5, 12) is x²-4x+7.

What is the vertex form of a quadratic equation?

Vertex form of the quadratic equation is used to find the coordinate of vertex points at which it crosses its symmetry.

The standard equation of the vertex form of quadratic is given as,

$y=a(x-h)^2+k$

Here, (h, k) is the vertex point.

The vertex of quadratic at (2, 3) and passing through the point (5, 12). Put the value of vertex point in the above equation,

$y=a(x-2)^2+3$

As the quadratic passes through the point (5, 12). Thus, put the value of this point,

$12=a(5-2)^2+3\\12-3=a(3)^2\\9=a\times9\\a=\dfrac{9}{9}\\a=1$

Put the value of a in the above expression,

$y=1(x-2)^2+3\\y=(x-2)^2+3\\y=x^2-4x+4+3\\y=x^2-4x+7$

Thus, the general form of the quadratic with vertex at (2, 3) and passing through the point (5, 12) is x²-4x+7.

Learn more about the vertex form here;

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