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MATH / The parabola with equation y=ax²+bx+c is graphed below:

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Answer published by the source. Consult the official source to check your work against its answer.

problem

The parabola with equation y=ax2+bx+cy=ax^2+bx+c is graphed below: [asy] unitsize(0.2 cm); xaxis(-5,9); yaxis(-7,2); real g(real x) { return -1/9*(x-2)^2+1; } draw(graph(g,-5,9)); dot((2,1)); label("Vertex: (2,1)(2,1)", (2,1), NE); dot((-4,-3)); label("(−4,−3)(-4,-3)", (-4,-3), W); [/asy] The zeros of the quadratic ax2+bx+cax^2 + bx + c are at x=mx=m and x=nx=n, where m>nm>n. What is m−nm-n?
Plain-text mathematical notation (without MathML)
The parabola with equation y=ax²+bx+c is graphed below:

[asy]
unitsize(0.2 cm);
xaxis(-5,9);

yaxis(-7,2);

real g(real x)

{

return -1/9*(x-2)^2+1;
}

draw(graph(g,-5,9));
dot((2,1));
label("Vertex: (2,1)", (2,1), NE);
dot((-4,-3));
label("(−4,−3)", (-4,-3), W);
[/asy]

The zeros of the quadratic ax²+bx+c are at x=m and x=n, where m>n. What is m−n?
Original LaTeX notation
The parabola with equation $y=ax^2+bx+c$ is graphed below:

[asy]
unitsize(0.2 cm);
xaxis(-5,9);

yaxis(-7,2);

real g(real x)

{

return -1/9*(x-2)^2+1;
}

draw(graph(g,-5,9));
dot((2,1));
label("Vertex: $(2,1)$", (2,1), NE);
dot((-4,-3));
label("$(-4,-3)$", (-4,-3), W);
[/asy]

The zeros of the quadratic $ax^2 + bx + c$ are at $x=m$ and $x=n$, where $m>n$. What is $m-n$?

level

Level 5

type

Algebra

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Source and history

task_id
d80ef636-8397-5ef9-bf3d-92ddb85707df
task_key
algebra--test--d80ef636-8397-5ef9-bf3d-92ddb85707df
task_revision_id
1
config / split
algebra / test

Official source

initial import