for the quadratic function ( f(x)=x^{2}+4x - 12 ), answer parts (a) through (f).\nis the graph concave up or…
for the quadratic function ( f(x)=x^{2}+4x - 12 ), answer parts (a) through (f).\nis the graph concave up or concave down?\nconcave down\nconcave up\n(b) find the y - intercept and the x - intercepts, if any.\nwhat is the y - intercept? select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the y - intercept is ( - 12 ).\n(type an integer or a simplified fraction.)\nb. there is no y - intercept.\nwhat is the x - intercept? select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the x - intercept(s) is/are\n(type an integer or a simplified fraction. use a comma to separate answers as needed.)\nb. there is/are no x - intercept(s).
Answer
Explanation:
Step1: Find the y - intercept
For a quadratic function (y = f(x)=ax^{2}+bx + c), the y - intercept is found by setting (x = 0). Substitute (x = 0) into (f(x)=x^{2}+4x - 12): (f(0)=0^{2}+4\times0 - 12=- 12)
Step2: Find the x - intercepts
Set (y = f(x)=0), so we have the quadratic equation (x^{2}+4x - 12 = 0). We can solve it using the quadratic formula (x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}) for the quadratic equation (ax^{2}+bx + c = 0). Here (a = 1), (b = 4), (c=-12). First, calculate the discriminant (\Delta=b^{2}-4ac=(4)^{2}-4\times1\times(-12)=16 + 48=64). Then (x=\frac{-4\pm\sqrt{64}}{2\times1}=\frac{-4\pm8}{2}). For the plus - sign: (x=\frac{-4 + 8}{2}=\frac{4}{2}=2). For the minus - sign: (x=\frac{-4-8}{2}=\frac{-12}{2}=-6).
Answer:
A. The y - intercept is (-12). A. The x - intercept(s) is/are (2,-6).