in which form of a quadratic equation is the vertex immediately apparent?\na. vertex form\nb. standard…

in which form of a quadratic equation is the vertex immediately apparent?\na. vertex form\nb. standard form\nc. intercept form\nd. linear form\n\nwhich statement about the standard form of a quadratic equation is incorrect?\na. it helps determine the direction the parabola opens.\nb. it can be used to identify the y - intercept.\nc. it directly reveals the x - intercepts.\nd. it looks like ( y = ax^{2}+bx + c ).

in which form of a quadratic equation is the vertex immediately apparent?\na. vertex form\nb. standard form\nc. intercept form\nd. linear form\n\nwhich statement about the standard form of a quadratic equation is incorrect?\na. it helps determine the direction the parabola opens.\nb. it can be used to identify the y - intercept.\nc. it directly reveals the x - intercepts.\nd. it looks like ( y = ax^{2}+bx + c ).

Answer

Brief Explanations:

  • For the first question:
    • The vertex form of a quadratic equation (y = a(x - h)^2 + k) has the vertex ((h,k)) directly in the equation.
    • The standard form (y=ax^{2}+bx + c) requires using the formula (x=-\frac{b}{2a}) to find the (x) - coordinate of the vertex and then substituting to find the (y) - coordinate.
    • The intercept form (y=a(x - p)(x - q)) is used to find the (x) - intercepts (p) and (q) easily.
    • A linear form is not a quadratic equation.
  • For the second question:
    • In the standard form (y = ax^{2}+bx + c), the sign of (a) determines the direction of the parabola (if (a>0), it opens up; if (a < 0), it opens down).
    • When (x = 0), (y=c), so (c) is the (y) - intercept.
    • The standard form (y=ax^{2}+bx + c) does not directly reveal the (x) - intercepts. We need to use the quadratic formula (x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}) or factor (if possible) to find the (x) - intercepts.
    • The standard form of a quadratic equation is (y = ax^{2}+bx + c).

Answer:

  1. A. Vertex form
  2. C. It directly reveals the x - intercepts.