Question

mfm2p
name: _____________ date: ___________

1. graph the following relation using speed graphing. 10 marks

y = x² + 4x - 5
graph grid with x from -10 to 10 and y from -10 to 10

Explanation:

Step1: Find vertex of parabola

For $y=ax^2+bx+c$, vertex $x=-\frac{b}{2a}$. Here $a=1, b=4$:
$x=-\frac{4}{2(1)}=-2$
Substitute $x=-2$ into equation:
$y=(-2)^2+4(-2)-5=4-8-5=-9$
Vertex: $(-2, -9)$

Step2: Find y-intercept

Set $x=0$:
$y=0^2+4(0)-5=-5$
Y-intercept: $(0, -5)$

Step3: Find x-intercepts

Set $y=0$:
$x^2+4x-5=0$
Factor: $(x+5)(x-1)=0$
Solutions: $x=-5, x=1$
X-intercepts: $(-5, 0), (1, 0)$

Step4: Plot key points & sketch

Plot vertex $(-2,-9)$, intercepts $(-5,0),(1,0),(0,-5)$, then draw a symmetric parabola passing through all points.

Answer:

The parabola has vertex $(-2, -9)$, x-intercepts $(-5, 0)$ and $(1, 0)$, y-intercept $(0, -5)$. When graphed, it is an upward-opening parabola passing through these key points on the provided coordinate grid.