How does the discriminant relate to the graphs of other types of functions?

Jul 21, 2023 ... If a>0 and b^(2)-4ac=0, then the graph of y=ax^(2)+bx+c touches x -axis and lies above x -axis. Jun 15, 2023 ... If the discriminant D < 0, then the quadratic equation ax 2 + bx + c = 0 will not have any real roots. Detailed step by step solution for k=(4ac-b^2)/(4a) F(z/Va- -b/2a) satisfies. (2) G(z)G(z + 1) = G(z2 + z - d), where d = (b2 - 4ac)/4a. The set Sd of roots of the polynomial G (z) is a finite nonempty set of ... May 30, 2023 ... The square root of the discriminant gives us (Edit: double?) the distance that each quadratic root lies either side of where the axis of symmetry crosses the x ... The discriminant (B2-4AC) is used to determine which conic section will result. If the discriminant is less than zero we have a circle (if A = C) or an ellipse; We know that b2 - 4ac is the discriminant (D). Thus, the vertex formula is: (h, k) = (-b/2a, -D/4a) where D = b2 ... Apr 11, 2018 ... For any equation of the form [ ax2 + bx + c = 0 ] the values of x ( the roots of the equation ) will always be [ ( -b ± ✓( b2 - 4ac ) ) / 2a ] ... Hence, the nature of the roots α and β of equation ax2 + bx + c = 0 depends on the quantity or expression (b2 – 4ac) under the square root sign. We say this ... Reduced forms. Consider a form ax2 + bxy + cy2. , with a, c > 0, and b2. -.