Answer:
-25
Step-by-step explanation:
(1) y = -2x²
(2) y = 2x² + k Subtract (1) from (2)
0 = 4x² + k Subtract 4x² from each side
k = -4x²
The parabolas are <em>symmetrical about the y-axis.</em>
Segment AB = 5, so x = +2.5 and x = +2.5.
k = -4(±2.5)² = -4 × 6.25 = -25
Considering the definition of zeros of a function, the zeros of the quadratic function f(x) = x² + 4x +9 do not exist.
<h3>Zeros of a function</h3>The points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.
In summary, the roots or zeros of the quadratic function are those values of x for which the expression is equal to 0. Graphically, the roots correspond to the abscissa of the points where the parabola intersects the x-axis.
In a quadratic function that has the form:
f(x)= ax² + bx + c
the zeros or roots are calculated by:
The quadratic function is f(x) = x² + 4x +9
Being:
the zeros or roots are calculated as:
and
If the content of the root is negative, the root will have no solution within the set of real numbers. Then has no solution.
Finally, the zeros of the quadratic function f(x) = x² + 4x +9 do not exist.
Learn more about the zeros of a quadratic function:
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