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Q: The line that cuts the graph of a quadratic function in half is called the axis of what?

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The zeros of a quadratic function, if they exist, are the values of the variable at which the graph crosses the horizontal axis.

The real solutions are the points at which the graph of the function crosses the x-axis. If the graph never crosses the x-axis, then the solutions are imaginary.

When the graph of a quadratic crosses the x-axis twice it means that the quadratic has two real roots. If the graph touches the x-axis at one point the quadratic has 1 repeated root. If the graph does not touch nor cross the x-axis, then the quadratic has no real roots, but it does have 2 complex roots.

Two.

It will cross the x-axis twice.

It will touch the x-axis and not cross it.

It will touch the x-axis once.

Once.

It would not touch or intersect the x-axis at all.

If the discriminant is negative, the equation has no real solution - in the graph, the parabola won't cross the x-axis.

...i need the answer to that too...

If the quadratic function is written as ax2 + bx + c then if a > 0 the function is cup shaped and if a < 0 it is cap shaped. (if a = 0 it is not a quadratic) if b2 > 4ac then the equation crosses the x-axis twice. if b2 = 4ac then the equation touches the x-axis (is a tangent to it). if b2 < 4ac then the equation does not cross the x-axis.

Yes it is possible. The solutions for a quadratic equation are the points where the function's graph touch the x-axis. There could be 2 places to that even if the graph looks different.

If a quadratic function has the points (-4,0) and (14,0), what is equation of the axis of symmetry?

No, it will be entirely above the x-axis if the coefficient of x2 > 0, or entirely below if the coeff is <0.

zero

When a function is multiplied by -1 its graph is reflected in the x-axis.

that's true

They will be on the horizontal x axis of the graph (look for the x-intercepts).

The wording is confusing, as a quadratic function is normally a function of one variable. If you mean the graph of y = f(x) where f is a quadratic function, then changes to the variable y will do some of those things. The transformation y --> -y will reflect the graph about the x-axis. The transformation y --> Ay (where A is real number) will cause the graph to stretch or shrink vertically. The transformation y --> y+A will translate it up or down.

The roots of a quadratic function are where the lies interescts with the x-axis. There can be as little as zero.

A parabola. An arch opening either north or south of the x-axis depending on the sign of the coefficient (negative opens down, positive opens up).

If the discriminant = 0 then the graph touches the x axis at one point If the discriminant > 0 then the graph touches the x axis at two ponits If the discriminant < 0 then the graph does not meet the x axis

On the x axis when y equals 0

Exactly halfway