Which quadratic inequality does the graph represent y <2x^2-8x+3
O y2 2x² + 8x+3
ys2x2 - 8x-3
O v2 2x2 - 8x+3

Option (1)

Step-by-step explanation:

Equation of a quadratic function,

y = a(x - h)² + k

Here (h, k) is the vertex

From the picture attached,

Vertex of the parabola is (2, -5)

So the equation of the function will be,

y = a(x - 2)² - 5

Since, the graph passes through a point (0, 3)

3 = a(0 - 2)² - 5

3 = 4a - 5

4a = 8

a = 2

Equation will be,

y = 2(x - 2)² - 5

y = 2(x² - 4x + 4) - 5

y = 2x² - 8x + 8 - 5

y = 2x² - 8x + 3

But the shaded area is outside the graph so the quadratic inequality will be,

y ≤ 2x² - 8x + 3

Option (1) will be the answer.