Question

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Answer 1

a) x = 2 and x = 4

Explanation:

A quadratic function is a mathematical function of the form f(x) = ax² + bx + c, where a, b, and c are constants and x represents the independent variable.

The solutions of a graphed quadratic function are the x-values of the points where the parabola crosses the x-axis.

These solutions are also known as the x-intercepts, roots, or zeros of the quadratic function.

From inspection of the given graph, the function crosses the x-axis at x = 2 and x = 4.

Therefore, the solutions of g(x) = -x² + 6x - 8 are:

• x = 2 and x = 4

Answer 2

x=2 and x=4.

Explanation:

The solution of g(x)=-x^2+6x-8 is the point where the graph of the function intersects the x-axis. This point is (4,0) and (2,0).

Therefore, the solution of g(x)=-x^2+6x-8 is x=4 and x=2.

Another method:

Similarly, we can find the value of x by factorization method too.

g(x)=x^2+6x-8

let g(x)=0

0=x^2+6x-8

x^2-6x+8=0

doing middle-term factorization:

x^2-(4+2)x+8=0

x^2-4x-2x+8=0

x(x-4)-2(x-4)=0

(x-4)(x-2)=0

either

x=4

0r

x=2

Therefore x=4 and x=2.