MTH 119W Intermediate Algebra Parabola Facts The Parabola y ...
MTH 119W Intermediate Algebra Parabola Facts The Parabola y ...
MTH 119W Intermediate Algebra Parabola Facts The Parabola y ...
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<strong>MTH</strong> <strong>119W</strong> <strong>Intermediate</strong> <strong>Algebra</strong><br />
<strong>Parabola</strong> <strong>Facts</strong><br />
<strong>The</strong> <strong>Parabola</strong> y = ax 2 + bx + c<br />
vertex:<br />
(<br />
− b )<br />
2a , c − b2<br />
4a<br />
a<br />
❄<br />
3a<br />
(0, c)<br />
❄<br />
5a<br />
x = − b<br />
2a<br />
❄<br />
1. <strong>The</strong> first coefficient a determines the scaling and orientation of the parabola<br />
(a) a > 0 - opens upward, a < 0 - opens downward<br />
(b) a = 2 - vertically stretched by a factor of 2<br />
(c) a = 1 - vertically compressed by a factor of 3<br />
3<br />
(d) <strong>The</strong> parabola pattern of 1a, 3a, 5a, . . . describes the vertical change for every<br />
step of 1 unit left and right of the vertex.<br />
❄<br />
7a<br />
2. <strong>The</strong> location of the vertex: x = − b<br />
2a ,<br />
3. <strong>The</strong> y-intercept: (0, c)<br />
y = c − b2<br />
4a<br />
4. <strong>The</strong> x-intercept(s), if there are any<br />
Solve the quadratic equation<br />
by factoring or the quadratic formula<br />
ax 2 + bx + c = 0<br />
x = −b ± √ b 2 − 4ac<br />
2a
<strong>MTH</strong> <strong>119W</strong> <strong>Intermediate</strong> <strong>Algebra</strong><br />
<strong>Parabola</strong> <strong>Facts</strong><br />
<strong>The</strong> <strong>Parabola</strong> y = a(x − h) 2 + k<br />
✻<br />
7a<br />
✻<br />
(<br />
0, ah 2 + k ) a<br />
5a<br />
✻<br />
3a<br />
✻<br />
x = h<br />
vertex: (h, k)<br />
1. <strong>The</strong> first coefficient a determines the scaling and orientation of the parabola<br />
(a) a > 0 - opens upward, a < 0 - opens downward<br />
(b) a = 2 - vertically stretched by a factor of 2<br />
(c) a = 1 - vertically compressed by a factor of 3<br />
3<br />
(d) <strong>The</strong> parabola pattern of 1a, 3a, 5a, . . . describes the vertical change for every<br />
step of 1 unit left and right of the vertex.<br />
2. <strong>The</strong> vertex: (h, k)<br />
3. <strong>The</strong> y-intercept: (0, ah 2 + k)<br />
4. <strong>The</strong> x-intercept(s), if there are any<br />
Solve the quadratic equation<br />
a(x − h) 2 + k = 0<br />
by using the square root property<br />
x = h ±<br />
√<br />
− k a
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