That's related to the fact that, for example, x squared is the same as (-x) squared. Note that any equation of the form "x squared + bx + c = 0", with constants a, b, and c can be rewritten as "(x - d) squared + f = 0", for possibly different constants d and f.
It is a turning point. It lies on the axis of symmetry.
Yes and this will happen when the discriminant of a quadratic equation is less than zero meaning it has no real roots.
Yes, they will.
It is x = +/- 2 depending on whether the second term in the equation is -12x or +12x.
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If a quadratic function has the points (-4,0) and (14,0), what is equation of the axis of symmetry?
The axis of symmetry of a quadratic function in the form (y = ax^2 + bx + c) can be found using the formula (x = -\frac{b}{2a}). This vertical line divides the parabola into two mirror-image halves. To find the corresponding (y)-coordinate, substitute the axis of symmetry value back into the quadratic function.
It is a turning point. It lies on the axis of symmetry.
It is the axis of symmetry.
The given quadratic function can be rewritten in standard form as ( y = 2(x - 3)^2 + 5 ). The axis of symmetry for a quadratic function in the form ( y = a(x - h)^2 + k ) is given by the line ( x = h ). Here, ( h = 3 ), so the axis of symmetry is ( x = 3 ).
Yes and this will happen when the discriminant of a quadratic equation is less than zero meaning it has no real roots.
Yes, they will.
A quadratic function is a noun. The plural form would be quadratic functions.
A quadratic function will have a degree of two.
When a quadratic function is graphed, the shape formed is called a parabola. This U-shaped curve can open either upwards or downwards, depending on the coefficient of the quadratic term. The vertex of the parabola represents the highest or lowest point of the graph, and the axis of symmetry is a vertical line that divides the parabola into two mirror-image halves.
No, a linear function does not have a line of symmetry. Linear functions, which can be expressed in the form (y = mx + b), produce straight lines on a graph that extend infinitely in both directions. Since these lines do not fold over onto themselves at any point, they lack a line of symmetry. Only certain types of functions, like quadratic functions, exhibit lines of symmetry.
It is x = +/- 2 depending on whether the second term in the equation is -12x or +12x.