2 Persamaan kuadrat x2 6 x 9 0 mempunyai nilai x1 x2 3 Bentuk persamaan kuadrat 2 x 7 3 x 2 mempunyai bentuk lain a x2 b x c 0 Tentukan nilai a b dan c nya 4 Akar akar persamaan kuadrat 3 x2 147 0...

#### Solution By Steps ***Step 1: Find the roots of the quadratic equation $x^{2}+6x+9=0$*** This is a perfect square trinomial: $(x+3)^{2}=0$. Therefore, $x=-3$ is the only root. ***Step 2: Express the quadratic $(2x-7)(3x+2)$ in the form $ax^{2}+bx+c$*** Expand the expression: $6x^{2}-17x-14$. So, $a=6$, $b=-17$, and $c=-14$. ***Step 3: Find the roots of the quadratic equation $3x^{2}-147=0$*** Factor out the equation: $3(x^{2}-49)=0$. The roots are $x=-7$ and $x=7$. ***Step 4: Condition for a quadratic equation to have equal roots*** For a quadratic equation to have equal roots, the discriminant ($b^{2}-4ac$) should be equal to 0. ***Step 5: Calculate the discriminant of $4x^{2}-15x+14=0$*** The discriminant is $(-15)^{2}-4(4)(14)=225-224=1$. ***Step 6: Find the $X$-intercepts of the quadratic function $y=7x^{2}-9x+2$*** Set $y=0$ and solve for $x$: $(7x-2)(x-1)=0$. The $X$-intercepts are $(2/7, 0)$ and $(1, 0)$. ***Step 7: Characteristics of the graph of $81-x^{2}$*** The graph is a parabola opening downwards with its vertex at $(0, 81)$. ***Step 8: Characteristics of the quadratic function $y=4x^{2}-13x+9$*** a. $a=4$, $b=-13$, $c=9$ b. $x_{1}+x_{2}=\frac{13}{4}$ c. $x_{1} \cdot x_{2}=\frac{9}{4}$ d. $x_{1}-x_{2}=3$ e. $(x_{1}+x_{2})^{2}=\frac{169}{16}$ f. Discriminant is $(-13)^{2}-4(4)(9)=25$ g. $X$-intercepts at $(\frac{3}{2}, 0)$ and $(\frac{3}{4}, 0)$ h. $Y$-intercept at $(0, 9)$ i. Axis of symmetry equation: $x=\frac{13}{8}$ j. Vertex at $(\frac{13}{8}, -\frac{7}{16})$ #### Final Answer 1. $x_{1}=-3$, $x_{2}=-3$ 2. $a=6$, $b=-17$, $c=-14$ 3. Roots are $x=-7$ and $x=7$ 4. Equal roots if discriminant is 0 5. Discriminant is 1 6. $(2/7, 0)$ and $(1, 0)$ 7. Parabola opening downwards with vertex at $(0, 81)$ 8. a. $a=4$, $b=-13$, $c=9$ b. $x_{1}+x_{2}=\frac{13}{4}$ c. $x_{1} \cdot x_{2}=\frac{9}{4}$ d. $x_{1}-x_{2}=3$ e. $(x_{1}+x_{2})^{2}=\frac{169}{16}$ f. Discriminant is 25 g. $X$-intercepts at $(\frac{3}{2}, 0)$ and $(\frac{3}{4}, 0)$ h. $Y$-intercept at $(0, 9)$ i. Axis of symmetry: $x=\frac{13}{8}$ j. Vertex at $(\frac{13}{8}, -\frac{7}{16})$ #### Key Concept Quadratic Equations #### Key Concept Explanation Quadratic equations involve terms up to the second power. Understanding their roots, discriminant, vertex, intercepts, and symmetry is crucial in solving problems involving parabolic functions.